Subgroups — C₃×C₅×#2241 #14275275

Order 1920.

280 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	C₃×C₅×#500	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#358	C₂	1	4	yes	maximal
4	C₃×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₅×#2241	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
7	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
8	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
9	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₃×C₅×C₁₆	C₂²	1	2	yes	—
11	C₃×C₅×#107	—	2	1	no	—
12	C₃×C₅×#107	C₂²	1	2	yes	—
13	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×#2241	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×#500	C₂×C₃	1	1	yes	characteristic
16	C₅×#494	C₂×C₃	1	1	yes	characteristic
17	C₅×#358	C₂×C₃	1	4	yes	—
18	C₄×C₅×C₁₆	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₈	—	2	2	no	—
20	C₂×C₃×C₅×Q₈	—	4	1	no	—
21	C₃×C₅×Q₁₆	—	2	4	no	—
22	C₃×C₅×Q₁₆	—	4	2	no	—
23	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
24	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
25	C₃×C₅×C₄⋊C₄	—	2	2	no	—
26	C₃×C₅×C₄⋊C₄	—	4	1	no	—
27	C₃×C₅×C₄⋊C₄	—	4	1	no	—
28	C₃×C₅×C₄⋊C₄	—	4	1	no	—
29	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
30	C₃×C₅×C₁₆	—	2	2	no	—
31	C₃×#500	C₂×C₅	1	1	yes	characteristic
32	C₃×#494	C₂×C₅	1	1	yes	characteristic
33	C₃×#358	C₂×C₅	1	4	yes	—
34	C₃×C₄×C₁₆	C₂×C₅	1	1	yes	characteristic
35	C₂×C₅×Q₁₆	—	2	1	no	—
36	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
37	C₅×C₄⋊Q₈	—	2	1	no	—
38	C₅×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₅×C₁₆	C₂²×C₃	1	2	yes	—
40	C₅×#107	—	2	1	no	—
41	C₅×#107	C₂²×C₃	1	2	yes	—
42	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
43	#2241	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
44	C₃×C₅×Q₈	—	4	2	no	—
45	C₃×C₅×Q₈	—	4	2	no	—
46	C₃×C₅×Q₈	—	8	2	no	—
47	C₂×C₃×C₄×C₅	—	4	2	no	—
48	C₂×C₃×C₄×C₅	—	4	2	no	—
49	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
52	C₃×C₅×C₈	SD₁₆	1	2	yes	—
53	C₃×C₅×C₈	#41	1	2	yes	—
54	C₂×C₃×Q₁₆	—	2	1	no	—
55	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
56	C₃×C₄⋊Q₈	—	2	1	no	—
57	C₃×C₄⋊Q₈	—	2	1	no	—
58	C₂×C₃×C₁₆	C₂²×C₅	1	2	yes	—
59	C₃×#107	—	2	1	no	—
60	C₃×#107	C₂²×C₅	1	2	yes	—
61	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
62	C₂×C₅×Q₈	—	2	2	no	—
63	C₂×C₅×Q₈	—	4	1	no	—
64	C₅×Q₁₆	—	2	4	no	—
65	C₅×Q₁₆	—	4	2	no	—
66	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
67	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
68	C₅×C₄⋊C₄	—	2	2	no	—
69	C₅×C₄⋊C₄	—	4	1	no	—
70	C₅×C₄⋊C₄	—	4	1	no	—
71	C₅×C₄⋊C₄	—	4	1	no	—
72	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
73	C₅×C₁₆	—	2	2	no	—
74	#500	C₂×C₃×C₅	1	1	yes	characteristic
75	#494	C₂×C₃×C₅	1	1	yes	characteristic
76	#358	C₂×C₃×C₅	1	4	yes	—
77	C₄×C₁₆	C₂×C₃×C₅	1	1	yes	characteristic
78	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
79	C₃×C₄×C₅	—	8	2	no	—
80	C₃×C₄×C₅	—	8	2	no	—
81	C₃×C₄×C₅	SD₃₂	1	2	yes	—
82	C₃×C₄×C₅	Q₃₂	1	2	yes	—
83	C₃×C₄×C₅	#124	1	1	yes	characteristic
84	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
85	C₂×C₃×Q₈	—	2	2	no	—
86	C₂×C₃×Q₈	—	4	1	no	—
87	C₃×Q₁₆	—	2	4	no	—
88	C₃×Q₁₆	—	4	2	no	—
89	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
90	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
91	C₃×C₄⋊C₄	—	2	2	no	—
92	C₃×C₄⋊C₄	—	4	1	no	—
93	C₃×C₄⋊C₄	—	4	1	no	—
94	C₃×C₄⋊C₄	—	4	1	no	—
95	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
96	C₃×C₁₆	—	2	2	no	—
97	C₅×Q₈	—	4	2	no	—
98	C₅×Q₈	—	4	2	no	—
99	C₅×Q₈	—	8	2	no	—
100	C₂×C₄×C₅	—	4	2	no	—
101	C₂×C₄×C₅	—	4	2	no	—
102	C₂×C₄×C₅	C₃×D₈	1	1	yes	characteristic
103	C₂×C₄×C₅	C₃×D₈	1	1	yes	characteristic
104	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
105	C₅×C₈	C₃×SD₁₆	1	2	yes	—
106	C₅×C₈	C₃×#41	1	2	yes	—
107	C₂×Q₁₆	—	2	1	no	—
108	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
109	C₄⋊Q₈	—	2	1	no	—
110	C₄⋊Q₈	—	2	1	no	—
111	C₂×C₁₆	C₂²×C₃×C₅	1	2	yes	—
112	#107	—	2	1	no	—
113	#107	C₂²×C₃×C₅	1	2	yes	—
114	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
115	C₂×C₃×C₅	#486	1	1	yes	characteristic
116	C₂×C₃×C₅	C₂×SD₃₂	1	1	yes	characteristic
117	C₂×C₃×C₅	C₂×Q₃₂	1	1	yes	characteristic
118	C₃×Q₈	—	4	2	no	—
119	C₃×Q₈	—	4	2	no	—
120	C₃×Q₈	—	8	2	no	—
121	C₂×C₃×C₄	—	4	2	no	—
122	C₂×C₃×C₄	—	4	2	no	—
123	C₂×C₃×C₄	C₅×D₈	1	1	yes	characteristic
124	C₂×C₃×C₄	C₅×D₈	1	1	yes	characteristic
125	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
126	C₃×C₈	C₅×SD₁₆	1	2	yes	—
127	C₃×C₈	C₅×#41	1	2	yes	—
128	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
129	C₄×C₅	—	8	2	no	—
130	C₄×C₅	—	8	2	no	—
131	C₄×C₅	C₃×SD₃₂	1	2	yes	—
132	C₄×C₅	C₃×Q₃₂	1	2	yes	—
133	C₄×C₅	C₃×#124	1	1	yes	characteristic
134	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
135	C₂×Q₈	—	2	2	no	—
136	C₂×Q₈	—	4	1	no	—
137	Q₁₆	—	2	4	no	—
138	Q₁₆	—	4	2	no	—
139	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
140	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
141	C₄⋊C₄	—	2	2	no	—
142	C₄⋊C₄	—	4	1	no	—
143	C₄⋊C₄	—	4	1	no	—
144	C₄⋊C₄	—	4	1	no	—
145	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
146	C₁₆	—	2	2	no	—
147	C₃×C₅	#2241	1	1	yes	characteristic, direct product factor, Hall
148	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
149	C₃×C₄	—	8	2	no	—
150	C₃×C₄	—	8	2	no	—
151	C₃×C₄	C₅×SD₃₂	1	2	yes	—
152	C₃×C₄	C₅×Q₃₂	1	2	yes	—
153	C₃×C₄	C₅×#124	1	1	yes	characteristic
154	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
155	C₂×C₅	C₃×#486	1	1	yes	characteristic
156	C₂×C₅	C₂×C₃×SD₃₂	1	1	yes	characteristic
157	C₂×C₅	C₂×C₃×Q₃₂	1	1	yes	characteristic
158	Q₈	—	4	2	no	—
159	Q₈	—	4	2	no	—
160	Q₈	—	8	2	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	4	2	no	—
163	C₂×C₄	C₃×C₅×D₈	1	1	yes	characteristic
164	C₂×C₄	C₃×C₅×D₈	1	1	yes	characteristic
165	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
166	C₈	C₃×C₅×SD₁₆	1	2	yes	—
167	C₈	C₃×C₅×#41	1	2	yes	—
168	C₂×C₃	C₅×#486	1	1	yes	characteristic
169	C₂×C₃	C₂×C₅×SD₃₂	1	1	yes	characteristic
170	C₂×C₃	C₂×C₅×Q₃₂	1	1	yes	characteristic
171	C₅	C₃×#2241	1	1	yes	characteristic, direct product factor, Sylow
172	C₂²	C₂×C₃×C₅×D₈	1	1	yes	characteristic
173	C₄	—	8	2	no	—
174	C₄	—	8	2	no	—
175	C₄	C₃×C₅×SD₃₂	1	2	yes	—
176	C₄	C₃×C₅×Q₃₂	1	2	yes	—
177	C₄	C₃×C₅×#124	1	1	yes	characteristic
178	C₄	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
179	C₃	C₅×#2241	1	1	yes	characteristic, direct product factor, Sylow
180	C₂	C₃×C₅×#486	1	1	yes	characteristic
181	C₂	C₂×C₃×C₅×SD₃₂	1	1	yes	characteristic
182	C₂	C₂×C₃×C₅×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ C₃×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₅×#2241	C₃	direct (N × H)
14. C₃×#2241	C₅	direct (N × H)
43. #2241	C₃×C₅	direct (N × H)
147. C₃×C₅	#2241	direct (N × H)
171. C₅	C₃×#2241	direct (N × H)
179. C₃	C₅×#2241	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×#500	2
C₃×C₅×#494	2
C₃×C₅×#358	2
C₃×C₄×C₅×C₁₆	2
C₅×#2241	3
C₃×#2241	5

Subgroups — C3×C5×#2241 #14275275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2241 #14275275