Subgroups — C₃×C₅×#1835 #14274869

Order 1920.

432 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	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#382	C₂	1	2	yes	maximal
3	C₃×C₅×#340	C₂	1	4	yes	maximal
4	C₅×#1835	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
6	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₃×C₄×C₅×C₈	C₄	1	4	yes	complemented
9	C₃×C₅×#95	—	2	4	no	—
10	C₃×#1835	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
12	C₅×#382	C₂×C₃	1	2	yes	—
13	C₅×#340	C₂×C₃	1	4	yes	—
14	C₂²×C₃×C₄×C₅	—	2	4	no	—
15	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
16	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
17	C₂×C₃×C₅×C₈	—	2	4	no	—
18	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
19	C₃×C₅×C₄⋊C₄	—	2	8	no	—
20	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
21	C₃×C₄²×C₅	Q₈	1	2	yes	—
22	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
23	C₃×#382	C₂×C₅	1	2	yes	—
24	C₃×#340	C₂×C₅	1	4	yes	—
25	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
26	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
27	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
28	C₄×C₅×C₈	C₃×C₄	1	4	yes	complemented
29	C₅×#95	—	2	4	no	—
30	#1835	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
32	C₂×C₃×C₄×C₅	—	2	4	no	—
33	C₂×C₃×C₄×C₅	—	4	4	no	—
34	C₂×C₃×C₄×C₅	—	4	8	no	—
35	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
36	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₃×C₄×C₅	#41	1	4	yes	—
39	C₃×C₅×C₈	—	2	4	no	—
40	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
41	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
42	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
43	C₃×C₄×C₈	C₄×C₅	1	4	yes	complemented
44	C₃×#95	—	2	4	no	—
45	C₂²×C₄×C₅	—	2	4	no	—
46	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
47	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
48	C₂×C₅×C₈	—	2	4	no	—
49	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
50	C₅×C₄⋊C₄	—	2	8	no	—
51	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
52	C₄²×C₅	C₃×Q₈	1	2	yes	—
53	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic
54	#382	C₂×C₃×C₅	1	2	yes	—
55	#340	C₂×C₃×C₅	1	4	yes	—
56	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₃×C₅	#124	1	2	yes	—
58	C₂²×C₃×C₅	#135	1	4	yes	—
59	C₃×C₄×C₅	—	2	4	no	—
60	C₃×C₄×C₅	—	8	4	no	—
61	C₃×C₄×C₅	#117	1	2	yes	—
62	C₃×C₄×C₅	#125	1	2	yes	—
63	C₂²×C₃×C₄	—	2	4	no	—
64	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
65	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
66	C₂×C₃×C₈	—	2	4	no	—
67	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
68	C₃×C₄⋊C₄	—	2	8	no	—
69	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
70	C₃×C₄²	C₅×Q₈	1	2	yes	—
71	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
72	C₂×C₄×C₅	—	2	4	no	—
73	C₂×C₄×C₅	—	4	4	no	—
74	C₂×C₄×C₅	—	4	8	no	—
75	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
76	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
77	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
78	C₂×C₄×C₅	C₃×#41	1	4	yes	—
79	C₅×C₈	—	2	4	no	—
80	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
81	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
82	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
83	C₄×C₈	C₃×C₄×C₅	1	4	yes	complemented
84	#95	—	2	4	no	—
85	C₂×C₃×C₅	#382	1	1	yes	characteristic
86	C₂×C₃×C₅	#427	1	2	yes	—
87	C₂×C₃×C₅	#488	1	4	yes	—
88	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄	—	2	4	no	—
90	C₂×C₃×C₄	—	4	4	no	—
91	C₂×C₃×C₄	—	4	8	no	—
92	C₂×C₃×C₄	C₅×C₄⋊C₄	1	4	yes	—
93	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
94	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
95	C₂×C₃×C₄	C₅×#41	1	4	yes	—
96	C₃×C₈	—	2	4	no	—
97	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
98	C₂²×C₅	C₃×#124	1	2	yes	—
99	C₂²×C₅	C₃×#135	1	4	yes	—
100	C₄×C₅	—	2	4	no	—
101	C₄×C₅	—	8	4	no	—
102	C₄×C₅	C₃×#117	1	2	yes	—
103	C₄×C₅	C₃×#125	1	2	yes	—
104	C₂²×C₄	—	2	4	no	—
105	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
106	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
107	C₂×C₈	—	2	4	no	—
108	C₂×C₈	C₂×C₃×C₄×C₅	1	4	yes	—
109	C₄⋊C₄	—	2	8	no	—
110	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
111	C₄²	C₃×C₅×Q₈	1	2	yes	—
112	C₃×C₅	#1835	1	1	yes	characteristic, direct product factor, Hall
113	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₃	C₅×#124	1	2	yes	—
115	C₂²×C₃	C₅×#135	1	4	yes	—
116	C₃×C₄	—	2	4	no	—
117	C₃×C₄	—	8	4	no	—
118	C₃×C₄	C₅×#117	1	2	yes	—
119	C₃×C₄	C₅×#125	1	2	yes	—
120	C₂×C₅	C₃×#382	1	1	yes	characteristic
121	C₂×C₅	C₃×#427	1	2	yes	—
122	C₂×C₅	C₃×#488	1	4	yes	—
123	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	4	4	no	—
126	C₂×C₄	—	4	8	no	—
127	C₂×C₄	C₃×C₅×C₄⋊C₄	1	4	yes	—
128	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
129	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
130	C₂×C₄	C₃×C₅×#41	1	4	yes	—
131	C₈	—	2	4	no	—
132	C₂×C₃	C₅×#382	1	1	yes	characteristic
133	C₂×C₃	C₅×#427	1	2	yes	—
134	C₂×C₃	C₅×#488	1	4	yes	—
135	C₅	C₃×#1835	1	1	yes	characteristic, direct product factor, Sylow
136	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
137	C₂²	C₃×C₅×#124	1	2	yes	—
138	C₂²	C₃×C₅×#135	1	4	yes	—
139	C₄	—	2	4	no	—
140	C₄	—	8	4	no	—
141	C₄	C₃×C₅×#117	1	2	yes	—
142	C₄	C₃×C₅×#125	1	2	yes	—
143	C₃	C₅×#1835	1	1	yes	characteristic, direct product factor, Sylow
144	C₂	C₃×C₅×#382	1	1	yes	characteristic
145	C₂	C₃×C₅×#427	1	2	yes	—
146	C₂	C₃×C₅×#488	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₅×#1835	C₃	direct (N × H)
8. C₃×C₄×C₅×C₈	C₄	semidirect
10. C₃×#1835	C₅	direct (N × H)
28. C₄×C₅×C₈	C₃×C₄	semidirect
30. #1835	C₃×C₅	direct (N × H)
43. C₃×C₄×C₈	C₄×C₅	semidirect
83. C₄×C₈	C₃×C₄×C₅	semidirect
112. C₃×C₅	#1835	direct (N × H)
135. C₅	C₃×#1835	direct (N × H)
143. C₃	C₅×#1835	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×C₈	2
C₃×C₅×#382	2
C₃×C₅×#340	2
C₅×#1835	3
C₃×#1835	5

Subgroups — C3×C5×#1835 #14274869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1835 #14274869