Subgroups — C₃×C₅×#2645 #14275679

Order 1920.

704 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#401	C₂	1	2	yes	maximal
2	C₃×C₅×#400	C₂	1	6	yes	maximal
3	C₃×C₅×#391	C₂	1	3	yes	maximal
4	C₃×C₅×#389	C₂	1	3	yes	maximal
5	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic
6	C₅×#2645	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	3	yes	—
9	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	6	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	—
11	C₃×C₅×#95	C₂²	1	3	yes	—
12	C₃×C₅×#95	C₂²	1	1	yes	characteristic
13	C₃×C₅×#95	C₂²	1	6	yes	—
14	C₃×C₅×#95	C₂²	1	6	yes	—
15	C₃×C₅×#95	C₂²	1	6	yes	—
16	C₃×#2645	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₅×#401	C₂×C₃	1	2	yes	—
18	C₅×#400	C₂×C₃	1	6	yes	—
19	C₅×#391	C₂×C₃	1	3	yes	—
20	C₅×#389	C₂×C₃	1	3	yes	—
21	C₅×#376	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×C₅×Q₈	—	2	6	no	—
23	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
24	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
25	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
26	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
27	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₄	—	2	6	no	—
29	C₃×C₅×C₄⋊C₄	—	4	6	no	—
30	C₃×C₄²×C₅	—	2	6	no	—
31	C₃×#401	C₂×C₅	1	2	yes	—
32	C₃×#400	C₂×C₅	1	6	yes	—
33	C₃×#391	C₂×C₅	1	3	yes	—
34	C₃×#389	C₂×C₅	1	3	yes	—
35	C₃×#376	C₂×C₅	1	1	yes	characteristic
36	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	3	yes	—
38	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	6	yes	—
39	C₂×C₄²×C₅	C₂²×C₃	1	3	yes	—
40	C₅×#95	C₂²×C₃	1	3	yes	—
41	C₅×#95	C₂²×C₃	1	1	yes	characteristic
42	C₅×#95	C₂²×C₃	1	6	yes	—
43	C₅×#95	C₂²×C₃	1	6	yes	—
44	C₅×#95	C₂²×C₃	1	6	yes	—
45	#2645	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
47	C₃×C₅×Q₈	—	4	4	no	—
48	C₂×C₃×C₄×C₅	—	2	3	no	—
49	C₂×C₃×C₄×C₅	—	2	3	no	—
50	C₂×C₃×C₄×C₅	—	2	6	no	—
51	C₂×C₃×C₄×C₅	—	2	6	no	—
52	C₂×C₃×C₄×C₅	—	2	3	no	—
53	C₂×C₃×C₄×C₅	—	2	6	no	—
54	C₂×C₃×C₄×C₅	—	2	6	no	—
55	C₂×C₃×C₄×C₅	—	2	3	no	—
56	C₂×C₃×C₄×C₅	—	2	6	no	—
57	C₂×C₃×C₄×C₅	#41	1	6	yes	—
58	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
59	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	3	yes	—
60	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	6	yes	—
61	C₂×C₃×C₄²	C₂²×C₅	1	3	yes	—
62	C₃×#95	C₂²×C₅	1	3	yes	—
63	C₃×#95	C₂²×C₅	1	1	yes	characteristic
64	C₃×#95	C₂²×C₅	1	6	yes	—
65	C₃×#95	C₂²×C₅	1	6	yes	—
66	C₃×#95	C₂²×C₅	1	6	yes	—
67	C₂×C₅×Q₈	—	2	6	no	—
68	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
69	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
70	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
71	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
72	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
73	C₅×C₄⋊C₄	—	2	6	no	—
74	C₅×C₄⋊C₄	—	4	6	no	—
75	C₄²×C₅	—	2	6	no	—
76	#401	C₂×C₃×C₅	1	2	yes	—
77	#400	C₂×C₃×C₅	1	6	yes	—
78	#391	C₂×C₃×C₅	1	3	yes	—
79	#389	C₂×C₃×C₅	1	3	yes	—
80	#376	C₂×C₃×C₅	1	1	yes	characteristic
81	C₂²×C₃×C₅	C₂×#41	1	3	yes	—
82	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
83	C₂²×C₃×C₅	2₋¹⁺⁴	1	3	yes	—
84	C₃×C₄×C₅	—	4	2	no	—
85	C₃×C₄×C₅	—	4	3	no	—
86	C₃×C₄×C₅	—	4	3	no	—
87	C₃×C₄×C₅	—	4	6	no	—
88	C₃×C₄×C₅	#126	1	4	yes	—
89	C₂×C₃×Q₈	—	2	6	no	—
90	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
91	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
92	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
93	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
94	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
95	C₃×C₄⋊C₄	—	2	6	no	—
96	C₃×C₄⋊C₄	—	4	6	no	—
97	C₃×C₄²	—	2	6	no	—
98	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
99	C₅×Q₈	—	4	4	no	—
100	C₂×C₄×C₅	—	2	3	no	—
101	C₂×C₄×C₅	—	2	3	no	—
102	C₂×C₄×C₅	—	2	6	no	—
103	C₂×C₄×C₅	—	2	6	no	—
104	C₂×C₄×C₅	—	2	3	no	—
105	C₂×C₄×C₅	—	2	6	no	—
106	C₂×C₄×C₅	—	2	6	no	—
107	C₂×C₄×C₅	—	2	3	no	—
108	C₂×C₄×C₅	—	2	6	no	—
109	C₂×C₄×C₅	C₃×#41	1	6	yes	—
110	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
111	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	3	yes	—
112	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	6	yes	—
113	C₂×C₄²	C₂²×C₃×C₅	1	3	yes	—
114	#95	C₂²×C₃×C₅	1	3	yes	—
115	#95	C₂²×C₃×C₅	1	1	yes	characteristic
116	#95	C₂²×C₃×C₅	1	6	yes	—
117	#95	C₂²×C₃×C₅	1	6	yes	—
118	#95	C₂²×C₃×C₅	1	6	yes	—
119	C₂×C₃×C₅	C₂×#126	1	1	yes	characteristic
120	C₂×C₃×C₅	#541	1	3	yes	—
121	C₂×C₃×C₅	#542	1	3	yes	—
122	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
123	C₃×Q₈	—	4	4	no	—
124	C₂×C₃×C₄	—	2	3	no	—
125	C₂×C₃×C₄	—	2	3	no	—
126	C₂×C₃×C₄	—	2	6	no	—
127	C₂×C₃×C₄	—	2	6	no	—
128	C₂×C₃×C₄	—	2	3	no	—
129	C₂×C₃×C₄	—	2	6	no	—
130	C₂×C₃×C₄	—	2	6	no	—
131	C₂×C₃×C₄	—	2	3	no	—
132	C₂×C₃×C₄	—	2	6	no	—
133	C₂×C₃×C₄	C₅×#41	1	6	yes	—
134	C₂²×C₅	C₂×C₃×#41	1	3	yes	—
135	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
136	C₂²×C₅	C₃×2₋¹⁺⁴	1	3	yes	—
137	C₄×C₅	—	4	2	no	—
138	C₄×C₅	—	4	3	no	—
139	C₄×C₅	—	4	3	no	—
140	C₄×C₅	—	4	6	no	—
141	C₄×C₅	C₃×#126	1	4	yes	—
142	C₂×Q₈	—	2	6	no	—
143	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
144	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
145	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
146	C₂²×C₄	C₂³×C₃×C₅	1	6	yes	—
147	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
148	C₄⋊C₄	—	2	6	no	—
149	C₄⋊C₄	—	4	6	no	—
150	C₄²	—	2	6	no	—
151	C₃×C₅	#2645	1	1	yes	characteristic, direct product factor, Hall
152	C₂²×C₃	C₂×C₅×#41	1	3	yes	—
153	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
154	C₂²×C₃	C₅×2₋¹⁺⁴	1	3	yes	—
155	C₃×C₄	—	4	2	no	—
156	C₃×C₄	—	4	3	no	—
157	C₃×C₄	—	4	3	no	—
158	C₃×C₄	—	4	6	no	—
159	C₃×C₄	C₅×#126	1	4	yes	—
160	C₂×C₅	C₂×C₃×#126	1	1	yes	characteristic
161	C₂×C₅	C₃×#541	1	3	yes	—
162	C₂×C₅	C₃×#542	1	3	yes	—
163	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
164	Q₈	—	4	4	no	—
165	C₂×C₄	—	2	3	no	—
166	C₂×C₄	—	2	3	no	—
167	C₂×C₄	—	2	6	no	—
168	C₂×C₄	—	2	6	no	—
169	C₂×C₄	—	2	3	no	—
170	C₂×C₄	—	2	6	no	—
171	C₂×C₄	—	2	6	no	—
172	C₂×C₄	—	2	3	no	—
173	C₂×C₄	—	2	6	no	—
174	C₂×C₄	C₃×C₅×#41	1	6	yes	—
175	C₂×C₃	C₂×C₅×#126	1	1	yes	characteristic
176	C₂×C₃	C₅×#541	1	3	yes	—
177	C₂×C₃	C₅×#542	1	3	yes	—
178	C₅	C₃×#2645	1	1	yes	characteristic, direct product factor, Sylow
179	C₂²	C₂×C₃×C₅×#41	1	3	yes	—
180	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
181	C₂²	C₃×C₅×2₋¹⁺⁴	1	3	yes	—
182	C₄	—	4	2	no	—
183	C₄	—	4	3	no	—
184	C₄	—	4	3	no	—
185	C₄	—	4	6	no	—
186	C₄	C₃×C₅×#126	1	4	yes	—
187	C₃	C₅×#2645	1	1	yes	characteristic, direct product factor, Sylow
188	C₂	C₂×C₃×C₅×#126	1	1	yes	characteristic
189	C₂	C₃×C₅×#541	1	3	yes	—
190	C₂	C₃×C₅×#542	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#2645	C₃	direct (N × H)
16. C₃×#2645	C₅	direct (N × H)
45. #2645	C₃×C₅	direct (N × H)
151. C₃×C₅	#2645	direct (N × H)
178. C₅	C₃×#2645	direct (N × H)
187. C₃	C₅×#2645	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×#401	2
C₃×C₅×#400	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#376	2
C₅×#2645	3
C₃×#2645	5

Subgroups — C3×C5×#2645 #14275679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2645 #14275679