Subgroups — C₃×C₅×#1845 #14274879

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#107	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×#1845	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×#107	—	2	8	no	—
10	C₃×C₄×C₅×C₈	C₄	1	4	yes	complemented
11	C₃×#1845	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×#107	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×#107	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×#107	—	2	8	no	—
33	C₄×C₅×C₈	C₃×C₄	1	4	yes	complemented
34	#1845	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	D₈	1	4	yes	—
40	C₂×C₃×C₄×C₅	Q₁₆	1	4	yes	—
41	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
43	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
44	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
45	C₃×C₅×C₈	C₄⋊C₄	1	8	yes	complemented
46	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
47	C₂×C₃×C₄⋊C₄	—	2	4	no	—
48	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
49	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
50	C₃×#107	—	2	8	no	—
51	C₃×C₄×C₈	C₄×C₅	1	4	yes	complemented
52	C₂²×C₄×C₅	—	2	4	no	—
53	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
54	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
55	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
56	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
57	C₂×C₅×C₈	C₃×Q₈	1	4	yes	—
58	C₅×C₄⋊C₄	—	2	8	no	—
59	C₅×C₄⋊C₄	—	4	8	no	—
60	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
61	C₄²×C₅	C₃×Q₈	1	2	yes	—
62	C₂×#107	C₂×C₃×C₅	1	4	yes	—
63	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic
64	#384	C₂×C₃×C₅	1	2	yes	—
65	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₃×C₅	#127	1	1	yes	characteristic
67	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
68	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
69	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
70	C₃×C₄×C₅	—	8	4	no	—
71	C₃×C₄×C₅	#107	1	8	yes	complemented
72	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
73	C₃×C₄×C₅	C₄⋊Q₈	1	2	yes	—
74	C₂²×C₃×C₄	—	2	4	no	—
75	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
76	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
77	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
78	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
79	C₂×C₃×C₈	C₅×Q₈	1	4	yes	—
80	C₃×C₄⋊C₄	—	2	8	no	—
81	C₃×C₄⋊C₄	—	4	8	no	—
82	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
83	C₃×C₄²	C₅×Q₈	1	2	yes	—
84	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
85	C₂×C₄×C₅	—	4	4	no	—
86	C₂×C₄×C₅	—	4	8	no	—
87	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
88	C₂×C₄×C₅	C₃×D₈	1	4	yes	—
89	C₂×C₄×C₅	C₃×Q₁₆	1	4	yes	—
90	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
91	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
92	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
93	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
94	C₅×C₈	C₃×C₄⋊C₄	1	8	yes	complemented
95	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
96	C₂×C₄⋊C₄	—	2	4	no	—
97	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
98	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
99	#107	—	2	8	no	—
100	C₄×C₈	C₃×C₄×C₅	1	4	yes	complemented
101	C₂×C₃×C₅	#384	1	1	yes	characteristic
102	C₂×C₃×C₅	C₂×#107	1	2	yes	—
103	C₂×C₃×C₅	#493	1	1	yes	characteristic
104	C₂×C₃×C₅	#494	1	1	yes	characteristic
105	C₂×C₃×C₅	#500	1	2	yes	—
106	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄	—	4	4	no	—
108	C₂×C₃×C₄	—	4	8	no	—
109	C₂×C₃×C₄	C₅×C₄⋊C₄	1	4	yes	—
110	C₂×C₃×C₄	C₅×D₈	1	4	yes	—
111	C₂×C₃×C₄	C₅×Q₁₆	1	4	yes	—
112	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
113	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
114	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
115	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
116	C₃×C₈	C₅×C₄⋊C₄	1	8	yes	complemented
117	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₅	C₃×#127	1	1	yes	characteristic
119	C₂²×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
120	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
121	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	—
122	C₄×C₅	—	8	4	no	—
123	C₄×C₅	C₃×#107	1	8	yes	complemented
124	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
125	C₄×C₅	C₃×C₄⋊Q₈	1	2	yes	—
126	C₂²×C₄	—	2	4	no	—
127	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
128	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
129	C₂×C₈	C₂×C₃×C₄×C₅	1	4	yes	—
130	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
131	C₂×C₈	C₃×C₅×Q₈	1	4	yes	—
132	C₄⋊C₄	—	2	8	no	—
133	C₄⋊C₄	—	4	8	no	—
134	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
135	C₄²	C₃×C₅×Q₈	1	2	yes	—
136	C₃×C₅	#1845	1	1	yes	characteristic, direct product factor, Hall
137	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
138	C₂²×C₃	C₅×#127	1	1	yes	characteristic
139	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
140	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
141	C₂²×C₃	C₂×C₅×Q₁₆	1	2	yes	—
142	C₃×C₄	—	8	4	no	—
143	C₃×C₄	C₅×#107	1	8	yes	complemented
144	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
145	C₃×C₄	C₅×C₄⋊Q₈	1	2	yes	—
146	C₂×C₅	C₃×#384	1	1	yes	characteristic
147	C₂×C₅	C₂×C₃×#107	1	2	yes	—
148	C₂×C₅	C₃×#493	1	1	yes	characteristic
149	C₂×C₅	C₃×#494	1	1	yes	characteristic
150	C₂×C₅	C₃×#500	1	2	yes	—
151	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
152	C₂×C₄	—	4	4	no	—
153	C₂×C₄	—	4	8	no	—
154	C₂×C₄	C₃×C₅×C₄⋊C₄	1	4	yes	—
155	C₂×C₄	C₃×C₅×D₈	1	4	yes	—
156	C₂×C₄	C₃×C₅×Q₁₆	1	4	yes	—
157	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
158	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
159	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
160	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
161	C₈	C₃×C₅×C₄⋊C₄	1	8	yes	complemented
162	C₂×C₃	C₅×#384	1	1	yes	characteristic
163	C₂×C₃	C₂×C₅×#107	1	2	yes	—
164	C₂×C₃	C₅×#493	1	1	yes	characteristic
165	C₂×C₃	C₅×#494	1	1	yes	characteristic
166	C₂×C₃	C₅×#500	1	2	yes	—
167	C₅	C₃×#1845	1	1	yes	characteristic, direct product factor, Sylow
168	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
169	C₂²	C₃×C₅×#127	1	1	yes	characteristic
170	C₂²	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
171	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
172	C₂²	C₂×C₃×C₅×Q₁₆	1	2	yes	—
173	C₄	—	8	4	no	—
174	C₄	C₃×C₅×#107	1	8	yes	complemented
175	C₄	C₂×C₃×C₅×C₄⋊C₄	1	2	yes	—
176	C₄	C₃×C₅×C₄⋊Q₈	1	2	yes	—
177	C₃	C₅×#1845	1	1	yes	characteristic, direct product factor, Sylow
178	C₂	C₃×C₅×#384	1	1	yes	characteristic
179	C₂	C₂×C₃×C₅×#107	1	2	yes	—
180	C₂	C₃×C₅×#493	1	1	yes	characteristic
181	C₂	C₃×C₅×#494	1	1	yes	characteristic
182	C₂	C₃×C₅×#500	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×#1845	C₃	direct (N × H)
10. C₃×C₄×C₅×C₈	C₄	semidirect
11. C₃×#1845	C₅	direct (N × H)
33. C₄×C₅×C₈	C₃×C₄	semidirect
34. #1845	C₃×C₅	direct (N × H)
45. C₃×C₅×C₈	C₄⋊C₄	semidirect
51. C₃×C₄×C₈	C₄×C₅	semidirect
71. C₃×C₄×C₅	#107	semidirect
94. C₅×C₈	C₃×C₄⋊C₄	semidirect
100. C₄×C₈	C₃×C₄×C₅	semidirect
116. C₃×C₈	C₅×C₄⋊C₄	semidirect
123. C₄×C₅	C₃×#107	semidirect
136. C₃×C₅	#1845	direct (N × H)
143. C₃×C₄	C₅×#107	semidirect
161. C₈	C₃×C₅×C₄⋊C₄	semidirect
167. C₅	C₃×#1845	direct (N × H)
174. C₄	C₃×C₅×#107	semidirect
177. C₃	C₅×#1845	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×#107	2
C₂×C₃×C₄×C₅×C₈	2
C₃×C₅×#384	2
C₅×#1845	3
C₃×#1845	5

Subgroups — C3×C5×#1845 #14274879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1845 #14274879