Subgroups — C₃×C₅×#1837 #14274871

Order 1920.

376 conjugacy classes of subgroups.

The subgroup lattice has 156 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×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#341	C₂	1	4	yes	maximal
4	C₅×#1837	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×C₄×C₅×C₈	C₄	1	2	yes	—
10	C₃×C₄×C₅×C₈	C₄	1	2	yes	—
11	C₃×#1837	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×#423	C₂×C₃	1	2	yes	—
13	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
14	C₅×#341	C₂×C₃	1	4	yes	—
15	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
16	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
17	C₃×C₅×M₁₆	—	2	8	no	—
18	C₂×C₃×C₅×C₈	—	2	4	no	—
19	C₂×C₃×C₅×C₈	—	2	4	no	—
20	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
21	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
22	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
23	C₃×C₄²×C₅	D₄	1	2	yes	—
24	C₃×#423	C₂×C₅	1	2	yes	—
25	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
26	C₃×#341	C₂×C₅	1	4	yes	—
27	C₂×C₅×M₁₆	C₂²×C₃	1	4	yes	—
28	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
29	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
30	C₅×C₄⋊C₈	—	2	4	no	—
31	C₄×C₅×C₈	C₃×C₄	1	2	yes	—
32	C₄×C₅×C₈	C₃×C₄	1	2	yes	—
33	#1837	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₃×C₄×C₅	—	2	4	no	—
36	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
37	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
38	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₅	#41	1	4	yes	—
41	C₃×C₅×C₈	—	2	4	no	—
42	C₃×C₅×C₈	—	4	4	no	—
43	C₂×C₃×M₁₆	C₂²×C₅	1	4	yes	—
44	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
45	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
46	C₃×C₄⋊C₈	—	2	4	no	—
47	C₃×C₄×C₈	C₄×C₅	1	2	yes	—
48	C₃×C₄×C₈	C₄×C₅	1	2	yes	—
49	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
50	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
51	C₅×M₁₆	—	2	8	no	—
52	C₂×C₅×C₈	—	2	4	no	—
53	C₂×C₅×C₈	—	2	4	no	—
54	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
55	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
56	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
57	C₄²×C₅	C₃×D₄	1	2	yes	—
58	#423	C₂×C₃×C₅	1	2	yes	—
59	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic
60	#341	C₂×C₃×C₅	1	4	yes	—
61	C₂²×C₃×C₅	—	2	2	no	—
62	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₃×C₅	#125	1	2	yes	—
64	C₃×C₄×C₅	—	2	2	no	—
65	C₃×C₄×C₅	#108	1	4	yes	—
66	C₃×C₄×C₅	#117	1	2	yes	—
67	C₃×C₄×C₅	#124	1	2	yes	—
68	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
69	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
70	C₃×M₁₆	—	2	8	no	—
71	C₂×C₃×C₈	—	2	4	no	—
72	C₂×C₃×C₈	—	2	4	no	—
73	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
74	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
75	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
76	C₃×C₄²	C₅×D₄	1	2	yes	—
77	C₂³×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
78	C₂×C₄×C₅	—	2	4	no	—
79	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
80	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
81	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
82	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
83	C₂×C₄×C₅	C₃×#41	1	4	yes	—
84	C₅×C₈	—	2	4	no	—
85	C₅×C₈	—	4	4	no	—
86	C₂×M₁₆	C₂²×C₃×C₅	1	4	yes	—
87	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
88	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
89	C₄⋊C₈	—	2	4	no	—
90	C₄×C₈	C₃×C₄×C₅	1	2	yes	—
91	C₄×C₈	C₃×C₄×C₅	1	2	yes	—
92	C₂×C₃×C₅	—	2	2	no	—
93	C₂×C₃×C₅	#382	1	1	yes	characteristic
94	C₂×C₃×C₅	C₂×#108	1	2	yes	—
95	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
96	C₂×C₃×C₄	—	2	4	no	—
97	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
98	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
99	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
100	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄	C₅×#41	1	4	yes	—
102	C₃×C₈	—	2	4	no	—
103	C₃×C₈	—	4	4	no	—
104	C₂²×C₅	—	2	2	no	—
105	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₅	C₃×#125	1	2	yes	—
107	C₄×C₅	—	2	2	no	—
108	C₄×C₅	C₃×#108	1	4	yes	—
109	C₄×C₅	C₃×#117	1	2	yes	—
110	C₄×C₅	C₃×#124	1	2	yes	—
111	C₂²×C₄	C₃×C₅×Q₈	1	2	yes	—
112	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
113	M₁₆	—	2	8	no	—
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	2	4	no	—
116	C₂×C₈	C₂×C₃×C₄×C₅	1	4	yes	—
117	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
118	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
119	C₄²	C₃×C₅×D₄	1	2	yes	—
120	C₃×C₅	#1837	1	1	yes	characteristic, direct product factor, Hall
121	C₂²×C₃	—	2	2	no	—
122	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₃	C₅×#125	1	2	yes	—
124	C₃×C₄	—	2	2	no	—
125	C₃×C₄	C₅×#108	1	4	yes	—
126	C₃×C₄	C₅×#117	1	2	yes	—
127	C₃×C₄	C₅×#124	1	2	yes	—
128	C₂×C₅	—	2	2	no	—
129	C₂×C₅	C₃×#382	1	1	yes	characteristic
130	C₂×C₅	C₂×C₃×#108	1	2	yes	—
131	C₂³	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
134	C₂×C₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
135	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
136	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
137	C₂×C₄	C₃×C₅×#41	1	4	yes	—
138	C₈	—	2	4	no	—
139	C₈	—	4	4	no	—
140	C₂×C₃	—	2	2	no	—
141	C₂×C₃	C₅×#382	1	1	yes	characteristic
142	C₂×C₃	C₂×C₅×#108	1	2	yes	—
143	C₅	C₃×#1837	1	1	yes	characteristic, direct product factor, Sylow
144	C₂²	—	2	2	no	—
145	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
146	C₂²	C₃×C₅×#125	1	2	yes	—
147	C₄	—	2	2	no	—
148	C₄	C₃×C₅×#108	1	4	yes	—
149	C₄	C₃×C₅×#117	1	2	yes	—
150	C₄	C₃×C₅×#124	1	2	yes	—
151	C₃	C₅×#1837	1	1	yes	characteristic, direct product factor, Sylow
152	C₂	—	2	2	no	—
153	C₂	C₃×C₅×#382	1	1	yes	characteristic
154	C₂	C₂×C₃×C₅×#108	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×#1837	C₃	direct (N × H)
11. C₃×#1837	C₅	direct (N × H)
33. #1837	C₃×C₅	direct (N × H)
120. C₃×C₅	#1837	direct (N × H)
143. C₅	C₃×#1837	direct (N × H)
151. C₃	C₅×#1837	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×C₄×C₅×C₈	2
C₃×C₅×#341	2
C₅×#1837	3
C₃×#1837	5

Subgroups — C3×C5×#1837 #14274871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1837 #14274871