Subgroups — C₅×D₃×C₄⋊C₈ #11750331

Order 960.

276 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×C₅×D₃×C₈	C₂	1	2	yes	maximal
2	C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×C₄⋊C₈	—	3	1	no	maximal, Hall
7	C₂×C₄×C₅×D₃	C₄	1	1	yes	characteristic
8	C₂×C₄×C₅×D₃	C₄	1	1	yes	characteristic
9	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
13	C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
14	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₃⋊C₈	C₂²	1	2	yes	—
16	C₅×D₃×C₈	—	2	4	no	—
17	D₃×C₄⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂²×C₅×C₈	—	3	2	no	—
19	C₂×C₄²×C₅	—	3	1	no	—
20	C₅×C₄⋊C₈	—	3	2	no	—
21	C₅×C₄⋊C₈	—	3	1	no	—
22	C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, direct product factor
23	C₂²×C₅×D₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
30	C₄×C₅×D₃	—	2	2	no	—
31	C₄×C₅×D₃	C₈	1	4	yes	complemented
32	C₄×C₅×D₃	D₄	1	2	yes	—
33	C₄×C₅×D₃	Q₈	1	2	yes	—
34	C₃×C₅×C₈	—	2	2	no	—
35	C₅×C₃⋊C₈	—	2	2	no	—
36	C₂×D₃×C₈	C₂×C₅	1	2	yes	—
37	C₄²×D₃	C₂×C₅	1	1	yes	characteristic
38	C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
39	Dic₃⋊C₈	C₂×C₅	1	2	yes	complemented
40	C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
41	C₂²×C₄×C₅	—	3	1	no	—
42	C₂²×C₄×C₅	—	3	1	no	—
43	C₂²×C₄×C₅	—	3	1	no	—
44	C₂×C₅×C₈	—	3	2	no	—
45	C₂×C₅×C₈	—	6	4	no	—
46	C₂×C₅×C₈	C₂×D₃	1	2	yes	—
47	C₄²×C₅	—	3	1	no	—
48	C₄²×C₅	—	3	1	no	—
49	C₄²×C₅	—	3	1	no	—
50	C₄²×C₅	C₂×D₃	1	1	yes	characteristic
51	C₂×C₄⋊C₈	—	3	1	no	Sylow
52	C₂²×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₅×D₃	C₄⋊C₄	1	2	yes	—
54	C₂×C₅×D₃	C₂×C₈	1	2	yes	—
55	C₂×C₅×D₃	M₁₆	1	2	yes	—
56	C₃×C₄×C₅	—	2	1	no	—
57	C₃×C₄×C₅	C₂×C₈	1	2	yes	complemented
58	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
59	C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
60	C₅×Dic₃	—	2	1	no	—
61	C₅×Dic₃	C₄⋊C₄	1	2	yes	—
62	C₅×Dic₃	C₂×C₈	1	2	yes	complemented
63	C₂×C₄×D₃	C₄×C₅	1	1	yes	characteristic
64	C₂×C₄×D₃	C₄×C₅	1	1	yes	characteristic
65	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
66	C₂×C₃×C₈	C₂²×C₅	1	2	yes	—
67	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
68	C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
69	C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
70	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
71	C₂×C₃⋊C₈	C₂²×C₅	1	2	yes	—
72	D₃×C₈	—	2	4	no	—
73	C₂³×C₅	—	3	1	no	—
74	C₂×C₄×C₅	—	3	1	no	—
75	C₂×C₄×C₅	—	3	1	no	—
76	C₂×C₄×C₅	—	3	4	no	—
77	C₂×C₄×C₅	—	3	2	no	—
78	C₂×C₄×C₅	—	3	2	no	—
79	C₂×C₄×C₅	—	3	1	no	—
80	C₂×C₄×C₅	—	6	2	no	—
81	C₂×C₄×C₅	C₄×D₃	1	1	yes	characteristic
82	C₂×C₄×C₅	C₄×D₃	1	1	yes	characteristic
83	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
84	C₅×C₈	—	2	2	no	—
85	C₅×C₈	—	6	2	no	—
86	C₂²×C₈	—	3	2	no	—
87	C₂×C₄²	—	3	1	no	—
88	C₄⋊C₈	—	3	2	no	—
89	C₄⋊C₈	—	3	1	no	—
90	C₄⋊C₈	C₅×D₃	1	1	yes	characteristic, direct product factor
91	C₂×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
93	C₂×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
94	C₅×D₃	C₄⋊C₈	1	4	yes	direct product factor
95	C₂²×D₃	C₂×C₄×C₅	1	1	yes	characteristic
96	C₂×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
97	C₂×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
98	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
99	C₂×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
100	C₂×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
101	C₂×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
102	C₄×D₃	—	2	2	no	—
103	C₄×D₃	C₅×C₈	1	4	yes	complemented
104	C₄×D₃	C₅×D₄	1	2	yes	—
105	C₄×D₃	C₅×Q₈	1	2	yes	—
106	C₃×C₈	—	2	2	no	—
107	C₃⋊C₈	—	2	2	no	—
108	C₂²×C₅	—	3	2	no	—
109	C₂²×C₅	—	3	2	no	—
110	C₂²×C₅	—	3	2	no	—
111	C₂²×C₅	C₂×C₄×D₃	1	1	yes	characteristic
112	C₄×C₅	—	2	1	no	—
113	C₄×C₅	—	3	2	no	—
114	C₄×C₅	—	3	2	no	—
115	C₄×C₅	—	6	1	no	—
116	C₄×C₅	D₃×C₈	1	2	yes	complemented
117	C₄×C₅	D₃×D₄	1	1	yes	characteristic
118	C₄×C₅	D₃×Q₈	1	1	yes	characteristic
119	C₂²×C₄	—	3	1	no	—
120	C₂²×C₄	—	3	1	no	—
121	C₂²×C₄	—	3	1	no	—
122	C₂×C₈	—	3	2	no	—
123	C₂×C₈	—	6	4	no	—
124	C₂×C₈	C₂×C₅×D₃	1	2	yes	—
125	C₄²	—	3	1	no	—
126	C₄²	—	3	1	no	—
127	C₄²	—	3	1	no	—
128	C₄²	C₂×C₅×D₃	1	1	yes	characteristic
129	C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
130	C₂²×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
131	C₂×D₃	C₅×C₄⋊C₄	1	2	yes	—
132	C₂×D₃	C₂×C₅×C₈	1	2	yes	—
133	C₂×D₃	C₅×M₁₆	1	2	yes	—
134	C₃×C₄	—	2	1	no	—
135	C₃×C₄	C₂×C₅×C₈	1	2	yes	complemented
136	C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
137	C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
138	Dic₃	—	2	1	no	—
139	Dic₃	C₅×C₄⋊C₄	1	2	yes	—
140	Dic₃	C₂×C₅×C₈	1	2	yes	complemented
141	C₂×C₅	—	3	4	no	—
142	C₂×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₅	C₂×D₃×C₈	1	1	yes	characteristic
144	C₂×C₅	D₃×M₁₆	1	1	yes	characteristic
145	C₂³	—	3	1	no	—
146	C₂×C₄	—	3	1	no	—
147	C₂×C₄	—	3	1	no	—
148	C₂×C₄	—	3	4	no	—
149	C₂×C₄	—	3	2	no	—
150	C₂×C₄	—	3	2	no	—
151	C₂×C₄	—	3	1	no	—
152	C₂×C₄	—	6	2	no	—
153	C₂×C₄	C₄×C₅×D₃	1	1	yes	characteristic
154	C₂×C₄	C₄×C₅×D₃	1	1	yes	characteristic
155	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
156	C₈	—	2	2	no	—
157	C₈	—	6	2	no	—
158	C₂×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
160	C₂×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
161	D₃	C₅×C₄⋊C₈	1	4	yes	direct product factor
162	C₅	D₃×C₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
163	C₂²	—	3	2	no	—
164	C₂²	—	3	2	no	—
165	C₂²	—	3	2	no	—
166	C₂²	C₂×C₄×C₅×D₃	1	1	yes	characteristic
167	C₄	—	2	1	no	—
168	C₄	—	3	2	no	—
169	C₄	—	3	2	no	—
170	C₄	—	6	1	no	—
171	C₄	C₅×D₃×C₈	1	2	yes	complemented
172	C₄	C₅×D₃×D₄	1	1	yes	characteristic
173	C₄	C₅×D₃×Q₈	1	1	yes	characteristic
174	C₃	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
175	C₂	—	3	4	no	—
176	C₂	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
177	C₂	C₂×C₅×D₃×C₈	1	1	yes	characteristic
178	C₂	C₅×D₃×M₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₄⋊C₈	C₂	semidirect
4. C₅×Dic₃⋊C₈	C₂	semidirect
5. C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
17. D₃×C₄⋊C₈	C₅	direct (N × H)
22. C₅×C₄⋊C₈	D₃	direct (N × H)
31. C₄×C₅×D₃	C₈	semidirect
38. C₃×C₄⋊C₈	C₂×C₅	semidirect
39. Dic₃⋊C₈	C₂×C₅	semidirect
40. C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
57. C₃×C₄×C₅	C₂×C₈	semidirect
62. C₅×Dic₃	C₂×C₈	semidirect
90. C₄⋊C₈	C₅×D₃	direct (N × H)
94. C₅×D₃	C₄⋊C₈	direct (N × H)
103. C₄×D₃	C₅×C₈	semidirect
116. C₄×C₅	D₃×C₈	semidirect
129. C₃×C₅	C₂×C₄⋊C₈	semidirect
135. C₃×C₄	C₂×C₅×C₈	semidirect
140. Dic₃	C₂×C₅×C₈	semidirect
161. D₃	C₅×C₄⋊C₈	direct (N × H)
162. C₅	D₃×C₄⋊C₈	direct (N × H)
171. C₄	C₅×D₃×C₈	semidirect
174. C₃	C₂×C₅×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×C₈	2
C₄²×C₅×D₃	2
C₃×C₅×C₄⋊C₈	2
C₅×Dic₃⋊C₈	2
C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×C₄⋊C₈	3
D₃×C₄⋊C₈	5

Subgroups — C5×D3×C4⋊C8 #11750331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₄⋊C₈ #11750331