Subgroups — C₃×#10600341 #14298859

Order 1920.

448 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×#382	C₂	1	1	yes	maximal, characteristic
2	C₃×#65224	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3935	C₂	1	1	yes	maximal, characteristic
4	C₃×#64749	C₂	1	4	yes	maximal
5	#10600341	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄⋊Dic₅	—	2	2	no	—
9	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
10	C₂²×C₃×#168	C₂²	1	2	yes	—
11	C₃×C₅×#95	—	2	2	no	—
12	C₃×#3935	C₄	1	4	yes	complemented
13	C₃×#1836	—	5	1	no	maximal, Hall
14	C₅×#382	C₂×C₃	1	1	yes	characteristic
15	#65224	C₂×C₃	1	1	yes	characteristic
16	C₂×#3935	C₂×C₃	1	1	yes	characteristic
17	#64749	C₂×C₃	1	4	yes	—
18	C₂²×C₃×C₄×C₅	—	2	2	no	—
19	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
20	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
21	C₂²×C₃×Dic₅	—	2	2	no	—
22	C₃×C₅×C₄⋊C₄	—	2	4	no	—
23	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
24	C₃×C₄²×C₅	Q₈	1	2	yes	—
25	C₃×C₄⋊Dic₅	—	2	4	no	—
26	C₃×C₄⋊Dic₅	—	4	4	no	—
27	C₂×C₃×#168	—	2	2	no	—
28	C₂×C₃×#168	—	2	2	no	—
29	C₂×C₃×#168	C₂×C₄	1	4	yes	—
30	C₂×C₃×#97	—	5	1	no	—
31	C₃×#384	—	5	1	no	—
32	C₃×#382	D₅	1	1	yes	characteristic
33	C₃×#340	—	5	4	no	—
34	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
35	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
36	C₂×C₄⋊Dic₅	—	2	2	no	—
37	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
38	C₂²×#168	C₂²×C₃	1	2	yes	—
39	C₅×#95	—	2	2	no	—
40	#3935	C₃×C₄	1	4	yes	complemented
41	#1836	—	5	1	no	Sylow
42	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₅	—	2	2	no	—
44	C₂×C₃×C₄×C₅	—	2	2	no	—
45	C₂×C₃×C₄×C₅	—	4	2	no	—
46	C₂×C₃×C₄×C₅	—	4	2	no	—
47	C₂×C₃×C₄×C₅	—	4	2	no	—
48	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
49	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	#41	1	2	yes	—
52	C₂×C₃×C₄×C₅	#41	1	2	yes	—
53	C₂×C₃×Dic₅	—	4	2	no	—
54	C₂×C₃×Dic₅	—	4	4	no	—
55	C₃×#168	—	2	4	no	—
56	C₂²×C₃×C₈	—	5	2	no	—
57	C₂×C₃×C₄⋊C₄	—	5	2	no	—
58	C₂×C₃×C₄⋊C₄	—	10	2	no	—
59	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
60	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
61	C₃×#97	—	5	4	no	—
62	C₃×#95	—	2	2	no	—
63	C₂²×C₄×C₅	—	2	2	no	—
64	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
65	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
66	C₂²×Dic₅	—	2	2	no	—
67	C₅×C₄⋊C₄	—	2	4	no	—
68	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
69	C₄²×C₅	C₃×Q₈	1	2	yes	—
70	C₄⋊Dic₅	—	2	4	no	—
71	C₄⋊Dic₅	—	4	4	no	—
72	C₂×#168	—	2	2	no	—
73	C₂×#168	—	2	2	no	—
74	C₂×#168	C₂×C₃×C₄	1	4	yes	—
75	C₂×#97	—	5	1	no	—
76	#384	—	5	1	no	—
77	#382	C₃×D₅	1	1	yes	characteristic
78	#340	—	5	4	no	—
79	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₃×C₅	#124	1	1	yes	characteristic
81	C₂²×C₃×C₅	#124	1	1	yes	characteristic
82	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
83	C₂²×C₃×C₅	#137	1	2	yes	—
84	C₃×C₄×C₅	—	2	4	no	—
85	C₃×C₄×C₅	—	8	2	no	—
86	C₃×C₄×C₅	#117	1	2	yes	—
87	C₃×C₄×C₅	#125	1	2	yes	—
88	C₃×Dic₅	—	8	2	no	—
89	C₂²×C₃×C₄	—	2	2	no	—
90	C₂²×C₃×C₄	—	10	2	no	—
91	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
92	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
93	C₂×C₃×C₈	—	5	4	no	—
94	C₂×C₃×C₈	—	10	2	no	—
95	C₂×C₃×C₈	—	10	2	no	—
96	C₃×C₄⋊C₄	—	2	4	no	—
97	C₃×C₄⋊C₄	—	10	4	no	—
98	C₃×C₄⋊C₄	—	20	4	no	—
99	C₃×C₄²	Dic₁₀	1	2	yes	—
100	C₃×C₄²	C₄×D₅	1	2	yes	—
101	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
102	C₂×C₄×C₅	—	2	2	no	—
103	C₂×C₄×C₅	—	2	2	no	—
104	C₂×C₄×C₅	—	4	2	no	—
105	C₂×C₄×C₅	—	4	2	no	—
106	C₂×C₄×C₅	—	4	2	no	—
107	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
108	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
109	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
110	C₂×C₄×C₅	C₃×#41	1	2	yes	—
111	C₂×C₄×C₅	C₃×#41	1	2	yes	—
112	C₂×Dic₅	—	4	2	no	—
113	C₂×Dic₅	—	4	4	no	—
114	#168	—	2	4	no	—
115	C₂²×C₈	—	5	2	no	—
116	C₂×C₄⋊C₄	—	5	2	no	—
117	C₂×C₄⋊C₄	—	10	2	no	—
118	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
119	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
120	#97	—	5	4	no	—
121	#95	—	2	2	no	—
122	C₂×C₃×C₅	#382	1	1	yes	characteristic
123	C₂×C₃×C₅	#428	1	2	yes	—
124	C₂×C₃×C₅	#489	1	2	yes	—
125	C₂×C₃×C₅	#490	1	1	yes	characteristic
126	C₂×C₃×C₅	#491	1	1	yes	characteristic
127	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
128	C₂×C₃×C₄	—	2	2	no	—
129	C₂×C₃×C₄	—	2	2	no	—
130	C₂×C₃×C₄	—	4	2	no	—
131	C₂×C₃×C₄	—	4	2	no	—
132	C₂×C₃×C₄	—	4	2	no	—
133	C₂×C₃×C₄	—	20	2	no	—
134	C₂×C₃×C₄	—	20	4	no	—
135	C₂×C₃×C₄	#683	1	4	yes	—
136	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
137	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
138	C₂×C₃×C₄	#711	1	2	yes	—
139	C₂×C₃×C₄	#713	1	2	yes	—
140	C₃×C₈	—	10	4	no	—
141	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
142	C₂²×C₅	C₃×#124	1	1	yes	characteristic
143	C₂²×C₅	C₃×#124	1	1	yes	characteristic
144	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
145	C₂²×C₅	C₃×#137	1	2	yes	—
146	C₄×C₅	—	2	4	no	—
147	C₄×C₅	—	8	2	no	—
148	C₄×C₅	C₃×#117	1	2	yes	—
149	C₄×C₅	C₃×#125	1	2	yes	—
150	Dic₅	—	8	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	10	2	no	—
153	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
154	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
155	C₂×C₈	—	5	4	no	—
156	C₂×C₈	—	10	2	no	—
157	C₂×C₈	—	10	2	no	—
158	C₄⋊C₄	—	2	4	no	—
159	C₄⋊C₄	—	10	4	no	—
160	C₄⋊C₄	—	20	4	no	—
161	C₄²	C₃×Dic₁₀	1	2	yes	—
162	C₄²	C₃×C₄×D₅	1	2	yes	—
163	C₃×C₅	#1836	1	1	yes	characteristic, complemented, Hall
164	C₂²×C₃	C₂×#683	1	1	yes	characteristic
165	C₂²×C₃	#4082	1	1	yes	characteristic
166	C₂²×C₃	#4093	1	1	yes	characteristic
167	C₂²×C₃	#4095	1	2	yes	—
168	C₂²×C₃	#4097	1	2	yes	—
169	C₃×C₄	—	2	4	no	—
170	C₃×C₄	—	8	2	no	—
171	C₃×C₄	—	40	2	no	—
172	C₃×C₄	#4036	1	2	yes	—
173	C₃×C₄	#4038	1	2	yes	—
174	C₂×C₅	C₃×#382	1	1	yes	characteristic
175	C₂×C₅	C₃×#428	1	2	yes	—
176	C₂×C₅	C₃×#489	1	2	yes	—
177	C₂×C₅	C₃×#490	1	1	yes	characteristic
178	C₂×C₅	C₃×#491	1	1	yes	characteristic
179	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	20	2	no	—
186	C₂×C₄	—	20	4	no	—
187	C₂×C₄	C₃×#683	1	4	yes	—
188	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
189	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
190	C₂×C₄	C₃×#711	1	2	yes	—
191	C₂×C₄	C₃×#713	1	2	yes	—
192	C₈	—	10	4	no	—
193	C₂×C₃	#65266	1	1	yes	characteristic
194	C₂×C₃	#65284	1	2	yes	—
195	C₂×C₃	#65344	1	2	yes	—
196	C₂×C₃	#65356	1	1	yes	characteristic
197	C₂×C₃	#65358	1	1	yes	characteristic
198	C₅	C₃×#1836	1	1	yes	characteristic, complemented, Sylow
199	C₂²	C₂×C₃×#683	1	1	yes	characteristic
200	C₂²	C₃×#4082	1	1	yes	characteristic
201	C₂²	C₃×#4093	1	1	yes	characteristic
202	C₂²	C₃×#4095	1	2	yes	—
203	C₂²	C₃×#4097	1	2	yes	—
204	C₄	—	2	4	no	—
205	C₄	—	8	2	no	—
206	C₄	—	40	2	no	—
207	C₄	C₃×#4036	1	2	yes	—
208	C₄	C₃×#4038	1	2	yes	—
209	C₃	#10600341	1	1	yes	characteristic, direct product factor, Sylow
210	C₂	C₃×#65266	1	1	yes	characteristic
211	C₂	C₃×#65284	1	2	yes	—
212	C₂	C₃×#65344	1	2	yes	—
213	C₂	C₃×#65356	1	1	yes	characteristic
214	C₂	C₃×#65358	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#382	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#382	D₅
hypocenter	C₅	C₃×#1836
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#382

Complements

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

N	H ≅ G/N	type
5. #10600341	C₃	direct (N × H)
12. C₃×#3935	C₄	semidirect
40. #3935	C₃×C₄	semidirect
163. C₃×C₅	#1836	semidirect
198. C₅	C₃×#1836	semidirect
209. C₃	#10600341	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×#382	2
C₃×#65224	2
C₂×C₃×#3935	2
C₃×#64749	2
#10600341	3
C₃×#1836	5

Subgroups — C3×#10600341 #14298859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600341 #14298859