Subgroups — C₅×#67808 #14278835

Order 1920.

256 conjugacy classes of subgroups.

The subgroup lattice has 148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#819	C₂	1	2	yes	maximal
3	C₅×#1381	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₂×C₅×#208	—	2	2	no	—
6	C₂×C₃×C₅×C₁₆	—	2	2	no	—
7	C₂×C₃×C₅×C₁₆	C₄	1	2	yes	—
8	C₅×#819	—	2	2	no	—
9	C₅×#819	C₄	1	4	yes	—
10	#67808	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₅×C₁₆	D₃	1	1	yes	characteristic
12	C₂×C₅×#108	—	3	2	no	—
13	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
14	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
16	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
17	C₂×C₃×C₅×C₈	Q₈	1	1	yes	characteristic
18	C₅×#208	—	2	4	no	—
19	C₅×#208	—	4	2	no	—
20	C₂×C₅×C₃⋊C₈	—	4	2	no	—
21	C₃×C₅×C₁₆	—	2	2	no	—
22	C₂²×C₃×C₁₆	C₂×C₅	1	1	yes	characteristic
23	C₂×#819	C₂×C₅	1	2	yes	—
24	C₂×C₅×M₁₆	—	6	2	no	—
25	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
26	C₂×C₅×C₁₆	—	2	2	no	—
27	C₂×C₅×C₁₆	Dic₃	1	2	yes	—
28	C₅×#108	—	3	4	no	—
29	C₅×#108	—	6	2	no	—
30	#1381	—	3	1	no	Sylow
31	C₂³×C₃×C₅	Q₁₆	1	1	yes	characteristic
32	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
33	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
35	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
36	C₃×C₅×C₈	C₄²	1	1	yes	characteristic
37	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
38	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
39	C₅×C₃⋊C₈	—	4	4	no	—
40	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
41	C₂×#208	—	2	2	no	—
42	C₂×C₃×C₁₆	—	2	2	no	—
43	C₂×C₃×C₁₆	C₄×C₅	1	2	yes	—
44	#819	—	2	2	no	—
45	#819	C₄×C₅	1	4	yes	—
46	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
47	C₅×M₁₆	—	6	4	no	—
48	C₅×M₁₆	—	12	2	no	—
49	C₂×C₅×C₈	—	12	2	no	—
50	C₂×C₅×C₈	Dic₆	1	1	yes	characteristic
51	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
52	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
53	C₂×C₅×C₈	#67	1	2	yes	—
54	C₅×C₁₆	—	2	2	no	—
55	C₂²×C₁₆	C₅×D₃	1	1	yes	characteristic
56	C₂×#108	—	3	2	no	—
57	C₂²×C₃×C₅	—	2	2	no	—
58	C₂²×C₃×C₅	#103	1	2	yes	—
59	C₂²×C₃×C₅	#107	1	1	yes	characteristic
60	C₃×C₄×C₅	#95	1	1	yes	characteristic
61	C₃×C₄×C₅	#102	1	2	yes	—
62	C₃×C₄×C₅	#106	1	1	yes	characteristic
63	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
64	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
65	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
66	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
67	C₂×C₃×C₈	C₅×Q₈	1	1	yes	characteristic
68	#208	—	2	4	no	—
69	#208	—	4	2	no	—
70	C₂×C₃⋊C₈	—	4	2	no	—
71	C₃×C₁₆	—	2	2	no	—
72	C₂³×C₅	Dic₁₂	1	1	yes	characteristic
73	C₂×C₄×C₅	#204	1	2	yes	—
74	C₂×C₄×C₅	D₂₄	1	1	yes	characteristic
75	C₂×C₄×C₅	C₄⋊Dic₃	1	1	yes	characteristic
76	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
77	C₅×C₈	—	12	4	no	—
78	C₅×C₈	C₄×Dic₃	1	1	yes	characteristic
79	C₅×C₈	Dic₃⋊C₄	1	2	yes	—
80	C₅×C₈	#217	1	1	yes	characteristic
81	C₂×M₁₆	—	6	2	no	—
82	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
83	C₂×C₁₆	—	2	2	no	—
84	C₂×C₁₆	C₅×Dic₃	1	2	yes	—
85	#108	—	3	4	no	—
86	#108	—	6	2	no	—
87	C₂×C₃×C₅	—	2	2	no	—
88	C₂×C₃×C₅	#340	1	1	yes	characteristic
89	C₂×C₃×C₅	#368	1	2	yes	—
90	C₂³×C₃	C₅×Q₁₆	1	1	yes	characteristic
91	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
92	C₂×C₃×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₃×C₄	C₅×D₈	1	1	yes	characteristic
94	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
95	C₃×C₈	C₄²×C₅	1	1	yes	characteristic
96	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
97	C₃×C₈	C₅×C₄⋊C₄	1	2	yes	—
98	C₃⋊C₈	—	4	4	no	—
99	C₂²×C₅	—	2	2	no	—
100	C₂²×C₅	#816	1	2	yes	—
101	C₂²×C₅	#818	1	1	yes	characteristic
102	C₄×C₅	#817	1	1	yes	characteristic
103	C₄×C₅	#821	1	2	yes	—
104	C₄×C₅	C₃⋊#95	1	1	yes	characteristic
105	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
106	M₁₆	—	6	4	no	—
107	M₁₆	—	12	2	no	—
108	C₂×C₈	—	12	2	no	—
109	C₂×C₈	C₅×Dic₆	1	1	yes	characteristic
110	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
111	C₂×C₈	C₂×C₅×Dic₃	1	1	yes	characteristic
112	C₂×C₈	C₅×#67	1	2	yes	—
113	C₁₆	—	2	2	no	—
114	C₃×C₅	#1381	1	1	yes	characteristic, complemented, Hall
115	C₂²×C₃	—	2	2	no	—
116	C₂²×C₃	C₅×#103	1	2	yes	—
117	C₂²×C₃	C₅×#107	1	1	yes	characteristic
118	C₃×C₄	C₅×#95	1	1	yes	characteristic
119	C₃×C₄	C₅×#102	1	2	yes	—
120	C₃×C₄	C₅×#106	1	1	yes	characteristic
121	C₂×C₅	—	2	2	no	—
122	C₂×C₅	#4506	1	2	yes	—
123	C₂×C₅	#4551	1	1	yes	characteristic
124	C₂³	C₅×Dic₁₂	1	1	yes	characteristic
125	C₂×C₄	C₅×#204	1	2	yes	—
126	C₂×C₄	C₅×D₂₄	1	1	yes	characteristic
127	C₂×C₄	C₅×C₄⋊Dic₃	1	1	yes	characteristic
128	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
129	C₈	—	12	4	no	—
130	C₈	C₄×C₅×Dic₃	1	1	yes	characteristic
131	C₈	C₅×Dic₃⋊C₄	1	2	yes	—
132	C₈	C₅×#217	1	1	yes	characteristic
133	C₂×C₃	—	2	2	no	—
134	C₂×C₃	C₅×#340	1	1	yes	characteristic
135	C₂×C₃	C₅×#368	1	2	yes	—
136	C₅	#67808	1	1	yes	characteristic, direct product factor, Sylow
137	C₂²	—	2	2	no	—
138	C₂²	C₅×#816	1	2	yes	—
139	C₂²	C₅×#818	1	1	yes	characteristic
140	C₄	C₅×#817	1	1	yes	characteristic
141	C₄	C₅×#821	1	2	yes	—
142	C₄	C₅×C₃⋊#95	1	1	yes	characteristic
143	C₃	C₅×#1381	1	1	yes	characteristic, complemented, Sylow
144	C₂	—	2	2	no	—
145	C₂	C₅×#4506	1	2	yes	—
146	C₂	C₅×#4551	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₂₄
commutator	C₃×C₈	C₄²×C₅
Frattini	C₂²×C₈	C₂×C₅×D₃
Fitting	C₂²×C₃×C₅×C₁₆	C₂
socle	C₂²×C₃×C₅	#107
prime radical	C₂³×C₃×C₅	Q₁₆
cosocle	C₂²×C₃×C₈	C₂²×C₅
hypercenter	C₂²×C₅×C₁₆	D₃
hypocenter	C₃	C₅×#1381
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂²×C₅×C₁₆

Complements

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

N	H ≅ G/N	type
10. #67808	C₅	direct (N × H)
114. C₃×C₅	#1381	semidirect
136. C₅	#67808	direct (N × H)
143. C₃	C₅×#1381	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₁₆	2
C₂×C₅×#819	2
C₅×#1381	3
#67808	5

Subgroups — C5×#67808 #14278835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#67808 #14278835