Subgroups — C₈×D₅×C₃⋊C₈ #14280313

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₄×D₅×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₈×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₈×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃⋊C₈×#168	C₂	1	2	yes	maximal, complemented
6	C₈²×D₅	—	3	1	no	maximal, Hall
7	C₂×C₃×C₈×D₅	C₄	1	2	yes	—
8	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
9	C₂×D₅×C₃⋊C₈	C₄	1	4	yes	—
10	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₄×C₃⋊#168	C₂²	1	2	yes	—
12	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
13	C₃×C₈×Dic₅	C₄	1	2	yes	—
14	C₃×C₄×#168	C₂²	1	1	yes	characteristic
15	Dic₅×C₃⋊C₈	C₄	1	4	yes	—
16	C₂×C₈×C₃⋊C₈	—	5	1	no	maximal, Hall
17	C₄×C₈×D₅	—	3	2	no	—
18	C₄×C₈×D₅	D₃	1	1	yes	characteristic
19	C₅×C₈²	—	3	1	no	—
20	C₈×#168	—	3	1	no	—
21	C₈×#168	—	3	2	no	—
22	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
25	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
26	C₂×C₃⋊#168	C₂×C₄	1	4	yes	—
27	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
28	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
29	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃×#168	C₂×C₄	1	2	yes	—
31	C₃×C₈×D₅	C₈	1	8	yes	complemented
32	D₅×C₃⋊C₈	C₈	1	16	yes	direct product factor
33	C₂×C₃×C₄×C₈	—	5	1	no	—
34	C₂×C₄×C₃⋊C₈	—	5	2	no	—
35	C₈×C₃⋊C₈	—	5	1	no	—
36	C₈×C₃⋊C₈	—	5	2	no	—
37	C₈×C₃⋊C₈	D₅	1	1	yes	characteristic, direct product factor
38	C₂×C₈×D₅	—	3	4	no	—
39	C₂×C₈×D₅	Dic₃	1	2	yes	—
40	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
41	C₄×C₅×C₈	—	3	2	no	—
42	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
43	C₈×Dic₅	—	3	4	no	—
44	C₈×Dic₅	Dic₃	1	2	yes	—
45	C₄×#168	—	3	2	no	—
46	C₄×#168	C₂×D₃	1	1	yes	characteristic
47	C₂×C₈²	—	15	1	no	Sylow
48	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
50	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
52	C₂×C₃×Dic₅	C₄²	1	2	yes	—
53	C₃×C₄×D₅	C₂×C₈	1	8	yes	—
54	C₃×C₄×D₅	C₂×C₈	1	4	yes	—
55	C₃×C₅×C₈	C₂×C₈	1	4	yes	complemented
56	C₃⋊#168	C₂×C₈	1	8	yes	complemented
57	C₃×#168	C₂×C₈	1	4	yes	complemented
58	C₅×C₃⋊C₈	C₂×C₈	1	8	yes	complemented
59	C₂²×C₃×C₈	—	5	2	no	—
60	C₂×C₃×C₄²	—	5	1	no	—
61	C₂²×C₃⋊C₈	—	5	4	no	—
62	C₃×C₄×C₈	—	5	2	no	—
63	C₃×C₄×C₈	—	5	1	no	—
64	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
65	C₄×C₃⋊C₈	—	5	2	no	—
66	C₄×C₃⋊C₈	—	5	4	no	—
67	C₄×C₃⋊C₈	C₂×D₅	1	2	yes	—
68	C₂×C₄×D₅	C₄×D₃	1	2	yes	—
69	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
70	C₂×C₅×C₈	—	3	4	no	—
71	C₂×C₅×C₈	C₂×Dic₃	1	2	yes	—
72	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
73	C₄×Dic₅	C₄×D₃	1	2	yes	—
74	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
75	C₂×#168	—	3	4	no	—
76	C₂×#168	C₂×Dic₃	1	2	yes	—
77	C₈×D₅	—	3	16	no	—
78	C₈×D₅	C₃⋊C₈	1	8	yes	direct product factor
79	C₂×C₄×C₈	—	5	1	no	—
80	C₂×C₄×C₈	—	15	2	no	—
81	C₈²	—	3	1	no	—
82	C₈²	—	15	2	no	—
83	C₈²	—	15	1	no	—
84	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
85	C₂×C₃×D₅	C₄×C₈	1	2	yes	—
86	C₂×C₃×D₅	C₄×C₈	1	4	yes	—
87	C₃×C₄×C₅	C₂²×C₈	1	4	yes	—
88	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
89	C₃×Dic₅	C₄×C₈	1	2	yes	—
90	C₃×Dic₅	C₄×C₈	1	4	yes	—
91	C₂²×C₃×C₄	—	5	2	no	—
92	C₂²×C₃×C₄	—	5	1	no	—
93	C₂×C₃×C₈	—	5	2	no	—
94	C₂×C₃×C₈	—	5	8	no	—
95	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
96	C₃×C₄²	—	5	2	no	—
97	C₃×C₄²	—	5	1	no	—
98	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
99	C₂×C₃⋊C₈	—	5	4	no	—
100	C₂×C₃⋊C₈	—	5	16	no	—
101	C₂×C₃⋊C₈	C₄×D₅	1	4	yes	—
102	C₂²×D₅	C₄×Dic₃	1	1	yes	characteristic
103	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
104	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
105	C₂×Dic₅	C₄×Dic₃	1	1	yes	characteristic
106	C₂×Dic₅	C₄×Dic₃	1	2	yes	—
107	C₄×D₅	D₃×C₈	1	8	yes	—
108	C₄×D₅	C₂×C₃⋊C₈	1	4	yes	—
109	C₅×C₈	—	3	8	no	—
110	C₅×C₈	C₂×C₃⋊C₈	1	4	yes	complemented
111	#168	—	3	8	no	—
112	#168	C₂×C₃⋊C₈	1	4	yes	complemented
113	C₂²×C₈	—	5	2	no	—
114	C₂²×C₈	—	15	4	no	—
115	C₂×C₄²	—	5	1	no	—
116	C₄×C₈	—	3	2	no	—
117	C₄×C₈	—	5	2	no	—
118	C₄×C₈	—	5	1	no	—
119	C₄×C₈	—	15	4	no	—
120	C₄×C₈	—	15	2	no	—
121	C₄×C₈	D₃×D₅	1	1	yes	characteristic
122	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
123	C₂×C₃×C₅	C₂×C₄×C₈	1	2	yes	—
124	C₃×D₅	C₈²	1	4	yes	complemented
125	C₂³×C₃	—	5	1	no	—
126	C₂×C₃×C₄	—	5	1	no	—
127	C₂×C₃×C₄	—	5	2	no	—
128	C₂×C₃×C₄	—	5	8	no	—
129	C₂×C₃×C₄	—	5	4	no	—
130	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
131	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
132	C₃×C₈	—	5	4	no	—
133	C₃×C₈	C₈×D₅	1	4	yes	complemented
134	C₃⋊C₈	—	5	8	no	—
135	C₃⋊C₈	C₈×D₅	1	8	yes	direct product factor
136	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
137	C₂×D₅	C₄×C₃⋊C₈	1	2	yes	—
138	C₂×D₅	C₈×Dic₃	1	4	yes	—
139	C₄×C₅	C₂×D₃×C₈	1	4	yes	—
140	C₄×C₅	C₂²×C₃⋊C₈	1	2	yes	—
141	Dic₅	C₄×C₃⋊C₈	1	2	yes	—
142	Dic₅	C₈×Dic₃	1	4	yes	—
143	C₂²×C₄	—	5	2	no	—
144	C₂²×C₄	—	5	1	no	—
145	C₂×C₈	—	3	4	no	—
146	C₂×C₈	—	5	2	no	—
147	C₂×C₈	—	5	8	no	—
148	C₂×C₈	—	15	16	no	—
149	C₂×C₈	—	15	4	no	—
150	C₂×C₈	D₅×Dic₃	1	2	yes	—
151	C₄²	—	5	2	no	—
152	C₄²	—	5	1	no	—
153	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
154	C₃×C₅	C₂×C₈²	1	1	yes	characteristic, complemented, Hall
155	C₂²×C₃	—	5	2	no	—
156	C₂²×C₃	—	5	4	no	—
157	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
158	C₃×C₄	—	5	2	no	—
159	C₃×C₄	—	5	4	no	—
160	C₃×C₄	C₂×C₈×D₅	1	4	yes	—
161	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
162	C₂×C₅	C₂×C₄×C₃⋊C₈	1	1	yes	characteristic
163	C₂×C₅	C₂×C₈×Dic₃	1	2	yes	—
164	D₅	C₈×C₃⋊C₈	1	4	yes	direct product factor
165	C₂³	—	5	1	no	—
166	C₂×C₄	—	5	1	no	—
167	C₂×C₄	—	5	2	no	—
168	C₂×C₄	—	5	8	no	—
169	C₂×C₄	—	5	4	no	—
170	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
171	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
172	C₈	—	3	8	no	—
173	C₈	—	5	4	no	—
174	C₈	—	15	8	no	—
175	C₈	D₅×C₃⋊C₈	1	4	yes	direct product factor
176	C₂×C₃	—	5	4	no	—
177	C₂×C₃	C₄×C₈×D₅	1	1	yes	characteristic
178	C₂×C₃	C₄×C₈×D₅	1	2	yes	—
179	C₅	C₂×C₈×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
180	C₂²	—	5	2	no	—
181	C₂²	—	5	4	no	—
182	C₂²	C₄×D₅×Dic₃	1	1	yes	characteristic
183	C₄	—	5	2	no	—
184	C₄	—	5	4	no	—
185	C₄	D₃×C₈×D₅	1	4	yes	—
186	C₄	C₂×D₅×C₃⋊C₈	1	2	yes	—
187	C₃	C₈²×D₅	1	1	yes	characteristic, complemented, Sylow
188	C₂	—	5	4	no	—
189	C₂	C₄×D₅×C₃⋊C₈	1	1	yes	characteristic
190	C₂	C₈×D₅×Dic₃	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₈	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₈²
Frattini	C₄²	C₂×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂²×C₃×D₅	C₄²
cosocle	C₃×C₄²×C₅	C₂³
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₈×C₃⋊#168	C₂	semidirect
4. C₅×C₈×C₃⋊C₈	C₂	semidirect
5. C₃⋊C₈×#168	C₂	semidirect
31. C₃×C₈×D₅	C₈	semidirect
32. D₅×C₃⋊C₈	C₈	direct (N × H)
37. C₈×C₃⋊C₈	D₅	direct (N × H)
55. C₃×C₅×C₈	C₂×C₈	semidirect
56. C₃⋊#168	C₂×C₈	semidirect
57. C₃×#168	C₂×C₈	semidirect
58. C₅×C₃⋊C₈	C₂×C₈	semidirect
78. C₈×D₅	C₃⋊C₈	direct (N × H)
110. C₅×C₈	C₂×C₃⋊C₈	semidirect
112. #168	C₂×C₃⋊C₈	semidirect
124. C₃×D₅	C₈²	semidirect
133. C₃×C₈	C₈×D₅	semidirect
135. C₃⋊C₈	C₈×D₅	direct (N × H)
154. C₃×C₅	C₂×C₈²	semidirect
164. D₅	C₈×C₃⋊C₈	direct (N × H)
175. C₈	D₅×C₃⋊C₈	direct (N × H)
179. C₅	C₂×C₈×C₃⋊C₈	semidirect
187. C₃	C₈²×D₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₈×D₅	2
C₄×D₅×C₃⋊C₈	2
C₈×C₃⋊#168	2
C₅×C₈×C₃⋊C₈	2
C₃⋊C₈×#168	2
C₈²×D₅	3
C₂×C₈×C₃⋊C₈	5

Subgroups — C8×D5×C3⋊C8 #14280313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×D₅×C₃⋊C₈ #14280313