Subgroups — C₃×C₅×#1844 #14274878

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#106	C₂	1	4	yes	maximal
2	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#384	C₂	1	2	yes	maximal
4	C₅×#1844	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	—	2	4	no	—
7	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₃×C₅×#106	—	2	8	no	—
10	C₃×C₄×C₅×C₈	C₄	1	4	yes	complemented
11	C₃×#1844	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×#106	C₂×C₃	1	4	yes	—
13	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
14	C₅×#384	C₂×C₃	1	2	yes	—
15	C₂²×C₃×C₄×C₅	—	2	4	no	—
16	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
17	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
18	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
19	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
20	C₂×C₃×C₅×C₈	Q₈	1	4	yes	—
21	C₃×C₅×C₄⋊C₄	—	2	8	no	—
22	C₃×C₅×C₄⋊C₄	—	4	8	no	—
23	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
24	C₃×C₄²×C₅	Q₈	1	2	yes	—
25	C₂×C₃×#106	C₂×C₅	1	4	yes	—
26	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
27	C₃×#384	C₂×C₅	1	2	yes	—
28	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
29	C₂×C₅×C₄⋊C₄	—	2	4	no	—
30	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
31	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
32	C₅×#106	—	2	8	no	—
33	C₄×C₅×C₈	C₃×C₄	1	4	yes	complemented
34	#1844	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
35	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
36	C₂×C₃×C₄×C₅	—	4	4	no	—
37	C₂×C₃×C₄×C₅	—	4	8	no	—
38	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
39	C₂×C₃×C₄×C₅	SD₁₆	1	8	yes	—
40	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
42	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
43	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
44	C₃×C₅×C₈	C₄⋊C₄	1	8	yes	complemented
45	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
46	C₂×C₃×C₄⋊C₄	—	2	4	no	—
47	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
48	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
49	C₃×#106	—	2	8	no	—
50	C₃×C₄×C₈	C₄×C₅	1	4	yes	complemented
51	C₂²×C₄×C₅	—	2	4	no	—
52	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
53	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
54	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
55	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
56	C₂×C₅×C₈	C₃×Q₈	1	4	yes	—
57	C₅×C₄⋊C₄	—	2	8	no	—
58	C₅×C₄⋊C₄	—	4	8	no	—
59	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
60	C₄²×C₅	C₃×Q₈	1	2	yes	—
61	C₂×#106	C₂×C₃×C₅	1	4	yes	—
62	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic
63	#384	C₂×C₃×C₅	1	2	yes	—
64	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂²×C₃×C₅	#127	1	1	yes	characteristic
66	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
67	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	—
68	C₃×C₄×C₅	—	8	4	no	—
69	C₃×C₄×C₅	#106	1	8	yes	complemented
70	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
71	C₃×C₄×C₅	C₄⋊Q₈	1	2	yes	—
72	C₂²×C₃×C₄	—	2	4	no	—
73	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
74	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
75	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
76	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
77	C₂×C₃×C₈	C₅×Q₈	1	4	yes	—
78	C₃×C₄⋊C₄	—	2	8	no	—
79	C₃×C₄⋊C₄	—	4	8	no	—
80	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
81	C₃×C₄²	C₅×Q₈	1	2	yes	—
82	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
83	C₂×C₄×C₅	—	4	4	no	—
84	C₂×C₄×C₅	—	4	8	no	—
85	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
86	C₂×C₄×C₅	C₃×SD₁₆	1	8	yes	—
87	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
88	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
89	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
90	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
91	C₅×C₈	C₃×C₄⋊C₄	1	8	yes	complemented
92	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
93	C₂×C₄⋊C₄	—	2	4	no	—
94	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
95	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
96	#106	—	2	8	no	—
97	C₄×C₈	C₃×C₄×C₅	1	4	yes	complemented
98	C₂×C₃×C₅	#384	1	1	yes	characteristic
99	C₂×C₃×C₅	C₂×#106	1	2	yes	—
100	C₂×C₃×C₅	#492	1	2	yes	—
101	C₂×C₃×C₅	#498	1	2	yes	—
102	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄	—	4	4	no	—
104	C₂×C₃×C₄	—	4	8	no	—
105	C₂×C₃×C₄	C₅×C₄⋊C₄	1	4	yes	—
106	C₂×C₃×C₄	C₅×SD₁₆	1	8	yes	—
107	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
109	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
110	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
111	C₃×C₈	C₅×C₄⋊C₄	1	8	yes	complemented
112	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
113	C₂²×C₅	C₃×#127	1	1	yes	characteristic
114	C₂²×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
115	C₂²×C₅	C₂×C₃×SD₁₆	1	4	yes	—
116	C₄×C₅	—	8	4	no	—
117	C₄×C₅	C₃×#106	1	8	yes	complemented
118	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
119	C₄×C₅	C₃×C₄⋊Q₈	1	2	yes	—
120	C₂²×C₄	—	2	4	no	—
121	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
122	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
123	C₂×C₈	C₂×C₃×C₄×C₅	1	4	yes	—
124	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
125	C₂×C₈	C₃×C₅×Q₈	1	4	yes	—
126	C₄⋊C₄	—	2	8	no	—
127	C₄⋊C₄	—	4	8	no	—
128	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
129	C₄²	C₃×C₅×Q₈	1	2	yes	—
130	C₃×C₅	#1844	1	1	yes	characteristic, direct product factor, Hall
131	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
132	C₂²×C₃	C₅×#127	1	1	yes	characteristic
133	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
134	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	—
135	C₃×C₄	—	8	4	no	—
136	C₃×C₄	C₅×#106	1	8	yes	complemented
137	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
138	C₃×C₄	C₅×C₄⋊Q₈	1	2	yes	—
139	C₂×C₅	C₃×#384	1	1	yes	characteristic
140	C₂×C₅	C₂×C₃×#106	1	2	yes	—
141	C₂×C₅	C₃×#492	1	2	yes	—
142	C₂×C₅	C₃×#498	1	2	yes	—
143	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
144	C₂×C₄	—	4	4	no	—
145	C₂×C₄	—	4	8	no	—
146	C₂×C₄	C₃×C₅×C₄⋊C₄	1	4	yes	—
147	C₂×C₄	C₃×C₅×SD₁₆	1	8	yes	—
148	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
149	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
150	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
151	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
152	C₈	C₃×C₅×C₄⋊C₄	1	8	yes	complemented
153	C₂×C₃	C₅×#384	1	1	yes	characteristic
154	C₂×C₃	C₂×C₅×#106	1	2	yes	—
155	C₂×C₃	C₅×#492	1	2	yes	—
156	C₂×C₃	C₅×#498	1	2	yes	—
157	C₅	C₃×#1844	1	1	yes	characteristic, direct product factor, Sylow
158	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
159	C₂²	C₃×C₅×#127	1	1	yes	characteristic
160	C₂²	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
161	C₂²	C₂×C₃×C₅×SD₁₆	1	4	yes	—
162	C₄	—	8	4	no	—
163	C₄	C₃×C₅×#106	1	8	yes	complemented
164	C₄	C₂×C₃×C₅×C₄⋊C₄	1	2	yes	—
165	C₄	C₃×C₅×C₄⋊Q₈	1	2	yes	—
166	C₃	C₅×#1844	1	1	yes	characteristic, direct product factor, Sylow
167	C₂	C₃×C₅×#384	1	1	yes	characteristic
168	C₂	C₂×C₃×C₅×#106	1	2	yes	—
169	C₂	C₃×C₅×#492	1	2	yes	—
170	C₂	C₃×C₅×#498	1	2	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×#1844	C₃	direct (N × H)
10. C₃×C₄×C₅×C₈	C₄	semidirect
11. C₃×#1844	C₅	direct (N × H)
33. C₄×C₅×C₈	C₃×C₄	semidirect
34. #1844	C₃×C₅	direct (N × H)
44. C₃×C₅×C₈	C₄⋊C₄	semidirect
50. C₃×C₄×C₈	C₄×C₅	semidirect
69. C₃×C₄×C₅	#106	semidirect
91. C₅×C₈	C₃×C₄⋊C₄	semidirect
97. C₄×C₈	C₃×C₄×C₅	semidirect
111. C₃×C₈	C₅×C₄⋊C₄	semidirect
117. C₄×C₅	C₃×#106	semidirect
130. C₃×C₅	#1844	direct (N × H)
136. C₃×C₄	C₅×#106	semidirect
152. C₈	C₃×C₅×C₄⋊C₄	semidirect
157. C₅	C₃×#1844	direct (N × H)
163. C₄	C₃×C₅×#106	semidirect
166. C₃	C₅×#1844	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×C₅×#106	2
C₂×C₃×C₄×C₅×C₈	2
C₃×C₅×#384	2
C₅×#1844	3
C₃×#1844	5

Subgroups — C3×C5×#1844 #14274878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1844 #14274878