Subgroups — C₃×#10619040 #14495604

Order 1920.

1860 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66034	C₂	1	5	yes	maximal, complemented
3	C₃×#66033	C₂	1	10	yes	maximal, complemented
4	C₃×#66025	C₂	1	10	yes	maximal, complemented
5	C₃×#66022	C₂	1	5	yes	maximal, complemented
6	#10619040	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×#125	C₂²	1	5	yes	—
8	C₃×C₅×#125	C₂²	1	10	yes	—
9	C₃×#4044	C₂²	1	20	yes	—
10	C₃×#4043	C₂²	1	10	yes	—
11	C₃×#4042	C₂²	1	20	yes	—
12	C₃×#4041	C₂²	1	10	yes	—
13	C₃×#4040	C₂²	1	20	yes	—
14	C₃×#4039	C₂²	1	10	yes	—
15	C₃×#4038	C₂²	1	10	yes	—
16	C₃×#4034	C₂²	1	10	yes	—
17	C₃×#4033	C₂²	1	10	yes	—
18	C₃×#4021	C₂²	1	10	yes	—
19	C₃×C₄²×D₅	C₂²	1	5	yes	—
20	C₃×#4016	C₂²	1	5	yes	—
21	C₃×#3531	—	5	1	no	maximal, Hall
22	C₅×#564	C₂×C₃	1	1	yes	characteristic, complemented
23	#66034	C₂×C₃	1	5	yes	complemented
24	#66033	C₂×C₃	1	10	yes	complemented
25	#66025	C₂×C₃	1	10	yes	complemented
26	#66022	C₂×C₃	1	5	yes	complemented
27	C₂×C₃×D₂₀	C₂³	1	10	yes	—
28	C₂×C₃×C₄×D₅	C₂³	1	5	yes	—
29	C₂×C₃×C₄×D₅	C₂³	1	10	yes	—
30	C₂×C₃×Dic₁₀	C₂³	1	10	yes	—
31	C₃×C₅×C₄⋊C₄	C₂³	1	10	yes	—
32	C₃×C₅×C₄⋊C₄	C₂³	1	10	yes	—
33	C₃×C₅×C₄⋊C₄	C₂³	1	10	yes	—
34	C₃×C₄²×C₅	C₂³	1	5	yes	—
35	C₃×#685	C₂³	1	20	yes	—
36	C₃×#685	C₂³	1	20	yes	—
37	C₃×C₄⋊Dic₅	C₂³	1	10	yes	—
38	C₃×#683	C₂³	1	20	yes	—
39	C₃×C₄×Dic₅	C₂³	1	10	yes	—
40	C₃×C₄×Dic₅	C₂³	1	5	yes	—
41	C₃×#564	D₅	1	1	yes	characteristic, complemented
42	C₃×#563	—	5	10	no	—
43	C₃×#562	—	5	5	no	—
44	C₃×#533	—	5	5	no	—
45	C₃×#529	—	5	10	no	—
46	C₅×#125	C₂²×C₃	1	5	yes	—
47	C₅×#125	C₂²×C₃	1	10	yes	—
48	#4044	C₂²×C₃	1	20	yes	—
49	#4043	C₂²×C₃	1	10	yes	—
50	#4042	C₂²×C₃	1	20	yes	—
51	#4041	C₂²×C₃	1	10	yes	—
52	#4040	C₂²×C₃	1	20	yes	—
53	#4039	C₂²×C₃	1	10	yes	—
54	#4038	C₂²×C₃	1	10	yes	—
55	#4034	C₂²×C₃	1	10	yes	—
56	#4033	C₂²×C₃	1	10	yes	—
57	#4021	C₂²×C₃	1	10	yes	—
58	C₄²×D₅	C₂²×C₃	1	5	yes	—
59	#4016	C₂²×C₃	1	5	yes	—
60	#3531	—	5	1	no	Sylow
61	C₂²×C₃×D₅	C₂⁴	1	5	yes	—
62	C₂×C₃×C₄×C₅	C₂⁴	1	10	yes	—
63	C₂×C₃×C₄×C₅	C₂⁴	1	5	yes	—
64	C₂×C₃×Dic₅	C₂⁴	1	10	yes	—
65	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
66	C₃×D₂₀	—	4	10	no	—
67	C₃×C₄×D₅	—	2	10	no	—
68	C₃×C₄×D₅	—	4	10	no	—
69	C₃×Dic₁₀	—	4	10	no	—
70	C₃×C₄⋊Q₈	—	5	10	no	—
71	C₃×#126	—	5	20	no	—
72	C₃×#125	—	5	5	no	—
73	C₃×#125	C₂×D₅	1	5	yes	—
74	C₃×#125	C₂×D₅	1	10	yes	—
75	C₃×#124	—	5	10	no	—
76	C₃×#123	—	5	20	no	—
77	C₃×C₂²⋊Q₈	—	5	20	no	—
78	C₃×C₂²⋊Q₈	—	5	10	no	—
79	C₃×#121	—	5	10	no	—
80	C₃×C₄×Q₈	—	5	10	no	—
81	C₃×C₄×D₄	—	5	10	no	—
82	C₃×#117	—	5	10	no	—
83	C₂×C₃×C₄²	—	5	5	no	—
84	C₂×D₂₀	C₂³×C₃	1	10	yes	—
85	C₂×C₄×D₅	C₂³×C₃	1	5	yes	—
86	C₂×C₄×D₅	C₂³×C₃	1	10	yes	—
87	C₂×Dic₁₀	C₂³×C₃	1	10	yes	—
88	C₅×C₄⋊C₄	C₂³×C₃	1	10	yes	—
89	C₅×C₄⋊C₄	C₂³×C₃	1	10	yes	—
90	C₅×C₄⋊C₄	C₂³×C₃	1	10	yes	—
91	C₄²×C₅	C₂³×C₃	1	5	yes	—
92	#685	C₂³×C₃	1	20	yes	—
93	#685	C₂³×C₃	1	20	yes	—
94	C₄⋊Dic₅	C₂³×C₃	1	10	yes	—
95	#683	C₂³×C₃	1	20	yes	—
96	C₄×Dic₅	C₂³×C₃	1	10	yes	—
97	C₄×Dic₅	C₂³×C₃	1	5	yes	—
98	#564	C₃×D₅	1	1	yes	characteristic, complemented
99	#563	—	5	10	no	—
100	#562	—	5	5	no	—
101	#533	—	5	5	no	—
102	#529	—	5	10	no	—
103	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
104	C₂×C₃×D₅	—	2	5	no	—
105	C₂×C₃×D₅	—	2	10	no	—
106	C₃×C₄×C₅	—	2	5	no	—
107	C₃×C₄×C₅	—	2	10	no	—
108	C₃×Dic₅	—	2	10	no	—
109	C₃×Dic₅	2₋¹⁺⁴	1	2	yes	—
110	C₂×C₃×Q₈	—	5	10	no	—
111	C₂×C₃×D₄	—	5	10	no	—
112	C₂²×C₃×C₄	—	5	5	no	—
113	C₂²×C₃×C₄	—	5	10	no	—
114	C₃×C₄⋊C₄	—	5	20	no	—
115	C₃×C₄⋊C₄	—	5	10	no	—
116	C₃×C₄⋊C₄	C₂²×D₅	1	10	yes	—
117	C₃×C₄⋊C₄	C₂²×D₅	1	10	yes	—
118	C₃×C₄⋊C₄	C₂²×D₅	1	10	yes	—
119	C₃×C₂²⋊C₄	—	5	20	no	—
120	C₃×C₂²⋊C₄	—	5	20	no	—
121	C₃×C₄²	—	5	10	no	—
122	C₃×C₄²	—	5	5	no	—
123	C₃×C₄²	C₂²×D₅	1	5	yes	—
124	C₂²×D₅	C₂⁴×C₃	1	5	yes	—
125	C₂×C₄×C₅	C₂⁴×C₃	1	10	yes	—
126	C₂×C₄×C₅	C₂⁴×C₃	1	5	yes	—
127	C₂×Dic₅	C₂⁴×C₃	1	10	yes	—
128	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
129	D₂₀	—	4	10	no	—
130	C₄×D₅	—	2	10	no	—
131	C₄×D₅	—	4	10	no	—
132	Dic₁₀	—	4	10	no	—
133	C₄⋊Q₈	—	5	10	no	—
134	#126	—	5	20	no	—
135	#125	—	5	5	no	—
136	#125	C₂×C₃×D₅	1	10	yes	—
137	#125	C₂×C₃×D₅	1	5	yes	—
138	#124	—	5	10	no	—
139	#123	—	5	20	no	—
140	C₂²⋊Q₈	—	5	10	no	—
141	C₂²⋊Q₈	—	5	20	no	—
142	#121	—	5	10	no	—
143	C₄×Q₈	—	5	10	no	—
144	C₄×D₄	—	5	10	no	—
145	#117	—	5	10	no	—
146	C₂×C₄²	—	5	5	no	—
147	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
148	C₂×C₃×C₅	#585	1	2	yes	—
149	C₃×D₅	—	4	5	no	—
150	C₂³×C₃	—	5	5	no	—
151	C₃×Q₈	—	20	10	no	—
152	C₃×D₄	—	20	10	no	—
153	C₂×C₃×C₄	—	5	1	no	—
154	C₂×C₃×C₄	—	5	10	no	—
155	C₂×C₃×C₄	—	10	10	no	—
156	C₂×C₃×C₄	—	20	10	no	—
157	C₂×C₃×C₄	C₂³×D₅	1	5	yes	—
158	C₂×C₃×C₄	C₂³×D₅	1	10	yes	—
159	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
160	C₂×D₅	—	2	5	no	—
161	C₂×D₅	—	2	10	no	—
162	C₄×C₅	—	2	5	no	—
163	C₄×C₅	—	2	10	no	—
164	Dic₅	—	2	10	no	—
165	Dic₅	C₃×2₋¹⁺⁴	1	2	yes	—
166	C₂×Q₈	—	5	10	no	—
167	C₂×D₄	—	5	10	no	—
168	C₂²×C₄	—	5	5	no	—
169	C₂²×C₄	—	5	10	no	—
170	C₄⋊C₄	—	5	10	no	—
171	C₄⋊C₄	—	5	20	no	—
172	C₄⋊C₄	C₂²×C₃×D₅	1	10	yes	—
173	C₄⋊C₄	C₂²×C₃×D₅	1	10	yes	—
174	C₄⋊C₄	C₂²×C₃×D₅	1	10	yes	—
175	C₂²⋊C₄	—	5	20	no	—
176	C₂²⋊C₄	—	5	20	no	—
177	C₄²	—	5	10	no	—
178	C₄²	—	5	5	no	—
179	C₄²	C₂²×C₃×D₅	1	5	yes	—
180	C₃×C₅	#3531	1	1	yes	characteristic, complemented, Hall
181	C₂²×C₃	—	10	5	no	—
182	C₂²×C₃	—	10	10	no	—
183	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
184	C₃×C₄	—	2	5	no	—
185	C₃×C₄	—	2	10	no	—
186	C₃×C₄	—	5	2	no	—
187	C₃×C₄	—	10	10	no	—
188	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₅	C₃×#585	1	2	yes	—
190	D₅	—	4	5	no	—
191	C₂³	—	5	5	no	—
192	Q₈	—	20	10	no	—
193	D₄	—	20	10	no	—
194	C₂×C₄	—	5	1	no	—
195	C₂×C₄	—	5	10	no	—
196	C₂×C₄	—	10	10	no	—
197	C₂×C₄	—	20	10	no	—
198	C₂×C₄	C₂³×C₃×D₅	1	5	yes	—
199	C₂×C₄	C₂³×C₃×D₅	1	10	yes	—
200	C₂×C₃	—	20	5	no	—
201	C₂×C₃	D₅×2₋¹⁺⁴	1	1	yes	characteristic
202	C₂×C₃	#66287	1	2	yes	—
203	C₅	C₃×#3531	1	1	yes	characteristic, complemented, Sylow
204	C₂²	—	10	5	no	—
205	C₂²	—	10	10	no	—
206	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
207	C₄	—	2	5	no	—
208	C₄	—	2	10	no	—
209	C₄	—	5	2	no	—
210	C₄	—	10	10	no	—
211	C₃	#10619040	1	1	yes	characteristic, direct product factor, Sylow
212	C₂	—	20	5	no	—
213	C₂	C₃×D₅×2₋¹⁺⁴	1	1	yes	characteristic
214	C₂	C₃×#66287	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#564	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#564	D₅
hypocenter	C₅	C₃×#3531
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#564

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#564	C₂	semidirect
2. C₃×#66034	C₂	semidirect
3. C₃×#66033	C₂	semidirect
4. C₃×#66025	C₂	semidirect
5. C₃×#66022	C₂	semidirect
6. #10619040	C₃	direct (N × H)
22. C₅×#564	C₂×C₃	semidirect
23. #66034	C₂×C₃	semidirect
24. #66033	C₂×C₃	semidirect
25. #66025	C₂×C₃	semidirect
26. #66022	C₂×C₃	semidirect
41. C₃×#564	D₅	semidirect
98. #564	C₃×D₅	semidirect
180. C₃×C₅	#3531	semidirect
203. C₅	C₃×#3531	semidirect
211. C₃	#10619040	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×#564	2
C₃×#66034	2
C₃×#66033	2
C₃×#66025	2
C₃×#66022	2
#10619040	3
C₃×#3531	5

Subgroups — C3×#10619040 #14495604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10619040 #14495604