Subgroups — C₃×#10598299 #14278836

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×C₃×#3951	C₂	1	2	yes	maximal
3	#10598299	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₂×C₃×#681	—	2	2	no	—
6	C₂×C₃×C₅×C₁₆	—	2	2	no	—
7	C₂×C₃×C₅×C₁₆	C₄	1	2	yes	—
8	C₃×#3951	—	2	2	no	—
9	C₃×#3951	C₄	1	4	yes	—
10	C₃×#1381	—	5	1	no	maximal, Hall
11	C₂²×C₅×C₁₆	C₂×C₃	1	1	yes	characteristic
12	C₂×#3951	C₂×C₃	1	2	yes	—
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	C₃×#681	—	2	4	no	—
19	C₃×#681	—	4	2	no	—
20	C₂×C₃×#168	—	4	2	no	—
21	C₃×C₅×C₁₆	—	2	2	no	—
22	C₂²×C₃×C₁₆	D₅	1	1	yes	characteristic
23	C₂×C₃×#108	—	5	2	no	—
24	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
25	C₂×#681	—	2	2	no	—
26	C₂×C₅×C₁₆	—	2	2	no	—
27	C₂×C₅×C₁₆	C₃×C₄	1	2	yes	—
28	#3951	—	2	2	no	—
29	#3951	C₃×C₄	1	4	yes	—
30	#1381	—	5	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	C₃×#168	—	4	4	no	—
40	C₂×C₃×M₁₆	—	10	2	no	—
41	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
42	C₂×C₃×C₁₆	—	2	2	no	—
43	C₂×C₃×C₁₆	Dic₅	1	2	yes	—
44	C₃×#108	—	5	4	no	—
45	C₃×#108	—	10	2	no	—
46	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
47	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
48	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
49	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
50	C₂×C₅×C₈	C₃×Q₈	1	1	yes	characteristic
51	#681	—	2	4	no	—
52	#681	—	4	2	no	—
53	C₂×#168	—	4	2	no	—
54	C₅×C₁₆	—	2	2	no	—
55	C₂²×C₁₆	C₃×D₅	1	1	yes	characteristic
56	C₂×#108	—	5	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	D₂₀	1	1	yes	characteristic
64	C₃×M₁₆	—	10	4	no	—
65	C₃×M₁₆	—	20	2	no	—
66	C₂×C₃×C₈	—	20	2	no	—
67	C₂×C₃×C₈	Dic₁₀	1	1	yes	characteristic
68	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
69	C₂×C₃×C₈	C₂×Dic₅	1	1	yes	characteristic
70	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
71	C₃×C₁₆	—	2	2	no	—
72	C₂³×C₅	C₃×Q₁₆	1	1	yes	characteristic
73	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
74	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₅	C₃×D₈	1	1	yes	characteristic
76	C₂×C₄×C₅	C₃×SD₁₆	1	2	yes	—
77	C₅×C₈	C₃×C₄²	1	1	yes	characteristic
78	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
79	C₅×C₈	C₃×C₄⋊C₄	1	2	yes	—
80	#168	—	4	4	no	—
81	C₂×M₁₆	—	10	2	no	—
82	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
83	C₂×C₁₆	—	2	2	no	—
84	C₂×C₁₆	C₃×Dic₅	1	2	yes	—
85	#108	—	5	4	no	—
86	#108	—	10	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	Dic₂₀	1	1	yes	characteristic
91	C₂×C₃×C₄	#677	1	2	yes	—
92	C₂×C₃×C₄	D₄₀	1	1	yes	characteristic
93	C₂×C₃×C₄	C₄⋊Dic₅	1	1	yes	characteristic
94	C₂×C₃×C₄	#685	1	2	yes	—
95	C₃×C₈	—	20	4	no	—
96	C₃×C₈	C₄×Dic₅	1	1	yes	characteristic
97	C₃×C₈	#683	1	2	yes	—
98	C₃×C₈	C₂²⋊Dic₅	1	1	yes	characteristic
99	C₂²×C₅	—	2	2	no	—
100	C₂²×C₅	C₃×#103	1	2	yes	—
101	C₂²×C₅	C₃×#107	1	1	yes	characteristic
102	C₄×C₅	C₃×#95	1	1	yes	characteristic
103	C₄×C₅	C₃×#102	1	2	yes	—
104	C₄×C₅	C₃×#106	1	1	yes	characteristic
105	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
106	M₁₆	—	10	4	no	—
107	M₁₆	—	20	2	no	—
108	C₂×C₈	—	20	2	no	—
109	C₂×C₈	C₃×Dic₁₀	1	1	yes	characteristic
110	C₂×C₈	C₃×C₄×D₅	1	2	yes	—
111	C₂×C₈	C₂×C₃×Dic₅	1	1	yes	characteristic
112	C₂×C₈	C₃×C₂²⋊D₅	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	#3948	1	2	yes	—
117	C₂²×C₃	#3950	1	1	yes	characteristic
118	C₃×C₄	#3949	1	1	yes	characteristic
119	C₃×C₄	#3953	1	2	yes	—
120	C₃×C₄	#3963	1	1	yes	characteristic
121	C₂×C₅	—	2	2	no	—
122	C₂×C₅	C₃×#340	1	1	yes	characteristic
123	C₂×C₅	C₃×#368	1	2	yes	—
124	C₂³	C₃×Dic₂₀	1	1	yes	characteristic
125	C₂×C₄	C₃×#677	1	2	yes	—
126	C₂×C₄	C₃×D₄₀	1	1	yes	characteristic
127	C₂×C₄	C₃×C₄⋊Dic₅	1	1	yes	characteristic
128	C₂×C₄	C₃×#685	1	2	yes	—
129	C₈	—	20	4	no	—
130	C₈	C₃×C₄×Dic₅	1	1	yes	characteristic
131	C₈	C₃×#683	1	2	yes	—
132	C₈	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
133	C₂×C₃	—	2	2	no	—
134	C₂×C₃	#64726	1	2	yes	—
135	C₂×C₃	#64771	1	1	yes	characteristic
136	C₅	C₃×#1381	1	1	yes	characteristic, complemented, Sylow
137	C₂²	—	2	2	no	—
138	C₂²	C₃×#3948	1	2	yes	—
139	C₂²	C₃×#3950	1	1	yes	characteristic
140	C₄	C₃×#3949	1	1	yes	characteristic
141	C₄	C₃×#3953	1	2	yes	—
142	C₄	C₃×#3963	1	1	yes	characteristic
143	C₃	#10598299	1	1	yes	characteristic, direct product factor, Sylow
144	C₂	—	2	2	no	—
145	C₂	C₃×#64726	1	2	yes	—
146	C₂	C₃×#64771	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄₀
commutator	C₅×C₈	C₃×C₄²
Frattini	C₂²×C₈	C₂×C₃×D₅
Fitting	C₂²×C₃×C₅×C₁₆	C₂
socle	C₂²×C₃×C₅	#107
prime radical	C₂³×C₃×C₅	Q₁₆
cosocle	C₂²×C₅×C₈	C₂²×C₃
hypercenter	C₂²×C₃×C₁₆	D₅
hypocenter	C₅	C₃×#1381
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂²×C₃×C₁₆

Complements

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

N	H ≅ G/N	type
3. #10598299	C₃	direct (N × H)
114. C₃×C₅	#1381	semidirect
136. C₅	C₃×#1381	semidirect
143. C₃	#10598299	direct (N × H)

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×C₃×#3951	2
#10598299	3
C₃×#1381	5

Subgroups — C3×#10598299 #14278836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10598299 #14278836