Subgroups — C₃×C₅×#1838 #14274872

Order 1920.

360 conjugacy classes of subgroups.

The subgroup lattice has 140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#423	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#341	C₂	1	4	yes	maximal
4	C₅×#1838	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×M₁₆	C₂²	1	4	yes	—
6	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₃×C₅×C₄⋊C₈	—	2	4	no	—
9	C₃×C₅×#97	C₄	1	4	yes	—
10	C₃×#1838	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×#423	C₂×C₃	1	2	yes	—
12	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic
13	C₅×#341	C₂×C₃	1	4	yes	—
14	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
15	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
16	C₃×C₅×M₁₆	—	2	8	no	—
17	C₂×C₃×C₅×C₈	—	2	4	no	—
18	C₂×C₃×C₅×C₈	—	2	4	no	—
19	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
20	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
21	C₃×C₄²×C₅	D₄	1	2	yes	—
22	C₃×#423	C₂×C₅	1	2	yes	—
23	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic
24	C₃×#341	C₂×C₅	1	4	yes	—
25	C₂×C₅×M₁₆	C₂²×C₃	1	4	yes	—
26	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
27	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
28	C₅×C₄⋊C₈	—	2	4	no	—
29	C₅×#97	C₃×C₄	1	4	yes	—
30	#1838	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₃×C₄×C₅	—	4	2	no	—
33	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
34	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
36	C₂×C₃×C₄×C₅	#41	1	4	yes	—
37	C₃×C₅×C₈	—	2	4	no	—
38	C₃×C₅×C₈	—	4	4	no	—
39	C₂×C₃×M₁₆	C₂²×C₅	1	4	yes	—
40	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
41	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
42	C₃×C₄⋊C₈	—	2	4	no	—
43	C₃×#97	C₄×C₅	1	4	yes	—
44	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
45	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
46	C₅×M₁₆	—	2	8	no	—
47	C₂×C₅×C₈	—	2	4	no	—
48	C₂×C₅×C₈	—	2	4	no	—
49	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
50	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
51	C₄²×C₅	C₃×D₄	1	2	yes	—
52	#423	C₂×C₃×C₅	1	2	yes	—
53	C₂×#97	C₂×C₃×C₅	1	1	yes	characteristic
54	#341	C₂×C₃×C₅	1	4	yes	—
55	C₂²×C₃×C₅	—	2	2	no	—
56	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₃×C₅	#125	1	2	yes	—
58	C₃×C₄×C₅	—	2	4	no	—
59	C₃×C₄×C₅	#117	1	2	yes	—
60	C₃×C₄×C₅	#124	1	2	yes	—
61	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
62	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
63	C₃×M₁₆	—	2	8	no	—
64	C₂×C₃×C₈	—	2	4	no	—
65	C₂×C₃×C₈	—	2	4	no	—
66	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
67	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
68	C₃×C₄²	C₅×D₄	1	2	yes	—
69	C₂³×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
70	C₂×C₄×C₅	—	4	2	no	—
71	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
72	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
73	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
74	C₂×C₄×C₅	C₃×#41	1	4	yes	—
75	C₅×C₈	—	2	4	no	—
76	C₅×C₈	—	4	4	no	—
77	C₂×M₁₆	C₂²×C₃×C₅	1	4	yes	—
78	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
79	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
80	C₄⋊C₈	—	2	4	no	—
81	#97	C₃×C₄×C₅	1	4	yes	—
82	C₂×C₃×C₅	—	2	2	no	—
83	C₂×C₃×C₅	#382	1	1	yes	characteristic
84	C₂×C₃×C₅	#430	1	2	yes	—
85	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
86	C₂×C₃×C₄	—	4	2	no	—
87	C₂×C₃×C₄	C₅×C₄⋊C₄	1	4	yes	—
88	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
89	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄	C₅×#41	1	4	yes	—
91	C₃×C₈	—	2	4	no	—
92	C₃×C₈	—	4	4	no	—
93	C₂²×C₅	—	2	2	no	—
94	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₅	C₃×#125	1	2	yes	—
96	C₄×C₅	—	2	4	no	—
97	C₄×C₅	C₃×#117	1	2	yes	—
98	C₄×C₅	C₃×#124	1	2	yes	—
99	C₂²×C₄	C₃×C₅×Q₈	1	2	yes	—
100	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
101	M₁₆	—	2	8	no	—
102	C₂×C₈	—	2	4	no	—
103	C₂×C₈	—	2	4	no	—
104	C₂×C₈	C₂×C₃×C₄×C₅	1	4	yes	—
105	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
106	C₄²	C₃×C₅×D₄	1	2	yes	—
107	C₃×C₅	#1838	1	1	yes	characteristic, direct product factor, Hall
108	C₂²×C₃	—	2	2	no	—
109	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
110	C₂²×C₃	C₅×#125	1	2	yes	—
111	C₃×C₄	—	2	4	no	—
112	C₃×C₄	C₅×#117	1	2	yes	—
113	C₃×C₄	C₅×#124	1	2	yes	—
114	C₂×C₅	—	2	2	no	—
115	C₂×C₅	C₃×#382	1	1	yes	characteristic
116	C₂×C₅	C₃×#430	1	2	yes	—
117	C₂³	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	C₃×C₅×C₄⋊C₄	1	4	yes	—
120	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
121	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
122	C₂×C₄	C₃×C₅×#41	1	4	yes	—
123	C₈	—	2	4	no	—
124	C₈	—	4	4	no	—
125	C₂×C₃	—	2	2	no	—
126	C₂×C₃	C₅×#382	1	1	yes	characteristic
127	C₂×C₃	C₅×#430	1	2	yes	—
128	C₅	C₃×#1838	1	1	yes	characteristic, direct product factor, Sylow
129	C₂²	—	2	2	no	—
130	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
131	C₂²	C₃×C₅×#125	1	2	yes	—
132	C₄	—	2	4	no	—
133	C₄	C₃×C₅×#117	1	2	yes	—
134	C₄	C₃×C₅×#124	1	2	yes	—
135	C₃	C₅×#1838	1	1	yes	characteristic, direct product factor, Sylow
136	C₂	—	2	2	no	—
137	C₂	C₃×C₅×#382	1	1	yes	characteristic
138	C₂	C₃×C₅×#430	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₃×C₅	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1838	C₃	direct (N × H)
10. C₃×#1838	C₅	direct (N × H)
30. #1838	C₃×C₅	direct (N × H)
107. C₃×C₅	#1838	direct (N × H)
128. C₅	C₃×#1838	direct (N × H)
135. C₃	C₅×#1838	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#423	2
C₂×C₃×C₅×#97	2
C₃×C₅×#341	2
C₅×#1838	3
C₃×#1838	5

Subgroups — C3×C5×#1838 #14274872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1838 #14274872