Subgroups — C₃×C₅×#1991 #14275025

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#340	C₂	1	4	yes	maximal
5	C₅×#1991	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
7	C₃×C₅×#125	—	2	2	no	—
8	C₃×C₅×#125	C₄	1	4	yes	complemented
9	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₅×C₈	—	2	2	no	—
14	C₃×C₅×#95	—	2	2	no	—
15	C₃×#1991	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic
17	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
18	C₅×#382	C₂×C₃	1	1	yes	characteristic
19	C₅×#340	C₂×C₃	1	4	yes	—
20	C₂²×C₃×C₄×C₅	—	2	2	no	—
21	C₂²×C₃×C₄×C₅	—	2	2	no	—
22	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
23	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₂×C₃×C₅×C₈	—	2	2	no	—
25	C₂×C₃×C₅×C₈	—	2	2	no	—
26	C₂×C₃×C₅×C₈	Q₈	1	4	yes	—
27	C₃×C₅×C₄⋊C₄	—	2	8	no	—
28	C₃×C₅×C₄⋊C₄	—	2	2	no	—
29	C₃×C₅×C₄⋊C₄	—	2	4	no	—
30	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
31	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
32	C₃×C₄²×C₅	D₄	1	2	yes	—
33	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic
34	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
35	C₃×#382	C₂×C₅	1	1	yes	characteristic
36	C₃×#340	C₂×C₅	1	4	yes	—
37	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
38	C₅×#125	—	2	2	no	—
39	C₅×#125	C₃×C₄	1	4	yes	complemented
40	C₂×C₅×C₄⋊C₄	—	2	2	no	—
41	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
42	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
43	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
44	C₄×C₅×C₈	—	2	2	no	—
45	C₅×#95	—	2	2	no	—
46	#1991	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
47	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
48	C₂×C₃×C₄×C₅	—	2	4	no	—
49	C₂×C₃×C₄×C₅	—	2	4	no	—
50	C₂×C₃×C₄×C₅	—	4	4	no	—
51	C₂×C₃×C₄×C₅	—	4	2	no	—
52	C₂×C₃×C₄×C₅	—	4	4	no	—
53	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
54	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
56	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
57	C₂×C₃×C₄×C₅	#41	1	2	yes	—
58	C₃×C₅×C₈	—	2	4	no	—
59	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
60	C₃×#125	—	2	2	no	—
61	C₃×#125	C₄×C₅	1	4	yes	complemented
62	C₂×C₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
64	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
65	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
66	C₃×C₄×C₈	—	2	2	no	—
67	C₃×#95	—	2	2	no	—
68	C₂²×C₄×C₅	—	2	2	no	—
69	C₂²×C₄×C₅	—	2	2	no	—
70	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
71	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
72	C₂×C₅×C₈	—	2	2	no	—
73	C₂×C₅×C₈	—	2	2	no	—
74	C₂×C₅×C₈	C₃×Q₈	1	4	yes	—
75	C₅×C₄⋊C₄	—	2	8	no	—
76	C₅×C₄⋊C₄	—	2	2	no	—
77	C₅×C₄⋊C₄	—	2	4	no	—
78	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
79	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
80	C₄²×C₅	C₃×D₄	1	2	yes	—
81	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic
82	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic
83	#382	C₂×C₃×C₅	1	1	yes	characteristic
84	#340	C₂×C₃×C₅	1	4	yes	—
85	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₃×C₅	#124	1	1	yes	characteristic
87	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
88	C₂²×C₃×C₅	#135	1	4	yes	—
89	C₃×C₄×C₅	—	2	4	no	—
90	C₃×C₄×C₅	—	4	4	no	—
91	C₃×C₄×C₅	—	8	2	no	—
92	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
93	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
94	C₂²×C₃×C₄	—	2	2	no	—
95	C₂²×C₃×C₄	—	2	2	no	—
96	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
97	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
98	C₂×C₃×C₈	—	2	2	no	—
99	C₂×C₃×C₈	—	2	2	no	—
100	C₂×C₃×C₈	C₅×Q₈	1	4	yes	—
101	C₃×C₄⋊C₄	—	2	8	no	—
102	C₃×C₄⋊C₄	—	2	2	no	—
103	C₃×C₄⋊C₄	—	2	4	no	—
104	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
105	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
106	C₃×C₄²	C₅×D₄	1	2	yes	—
107	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
108	C₂×C₄×C₅	—	2	4	no	—
109	C₂×C₄×C₅	—	2	4	no	—
110	C₂×C₄×C₅	—	4	4	no	—
111	C₂×C₄×C₅	—	4	2	no	—
112	C₂×C₄×C₅	—	4	4	no	—
113	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
114	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
115	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
116	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
117	C₂×C₄×C₅	C₃×#41	1	2	yes	—
118	C₅×C₈	—	2	4	no	—
119	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
120	#125	—	2	2	no	—
121	#125	C₃×C₄×C₅	1	4	yes	complemented
122	C₂×C₄⋊C₄	—	2	2	no	—
123	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
124	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
125	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
126	C₄×C₈	—	2	2	no	—
127	#95	—	2	2	no	—
128	C₂×C₃×C₅	#391	1	1	yes	characteristic
129	C₂×C₃×C₅	#416	1	2	yes	—
130	C₂×C₃×C₅	#488	1	2	yes	—
131	C₂×C₃×C₅	#499	1	2	yes	—
132	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
133	C₂×C₃×C₄	—	2	4	no	—
134	C₂×C₃×C₄	—	2	4	no	—
135	C₂×C₃×C₄	—	4	4	no	—
136	C₂×C₃×C₄	—	4	2	no	—
137	C₂×C₃×C₄	—	4	4	no	—
138	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
139	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
140	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
142	C₂×C₃×C₄	C₅×#41	1	2	yes	—
143	C₃×C₈	—	2	4	no	—
144	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₅	C₃×#124	1	1	yes	characteristic
146	C₂²×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
147	C₂²×C₅	C₃×#135	1	4	yes	—
148	C₄×C₅	—	2	4	no	—
149	C₄×C₅	—	4	4	no	—
150	C₄×C₅	—	8	2	no	—
151	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
152	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	2	2	no	—
155	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
156	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	C₃×C₅×Q₈	1	4	yes	—
160	C₄⋊C₄	—	2	8	no	—
161	C₄⋊C₄	—	2	2	no	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
164	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
165	C₄²	C₃×C₅×D₄	1	2	yes	—
166	C₃×C₅	#1991	1	1	yes	characteristic, direct product factor, Hall
167	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₃	C₅×#124	1	1	yes	characteristic
169	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
170	C₂²×C₃	C₅×#135	1	4	yes	—
171	C₃×C₄	—	2	4	no	—
172	C₃×C₄	—	4	4	no	—
173	C₃×C₄	—	8	2	no	—
174	C₃×C₄	C₄×C₅×Q₈	1	2	yes	—
175	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
176	C₂×C₅	C₃×#391	1	1	yes	characteristic
177	C₂×C₅	C₃×#416	1	2	yes	—
178	C₂×C₅	C₃×#488	1	2	yes	—
179	C₂×C₅	C₃×#499	1	2	yes	—
180	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	—	2	4	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	4	yes	—
187	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
188	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
189	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
190	C₂×C₄	C₃×C₅×#41	1	2	yes	—
191	C₈	—	2	4	no	—
192	C₂×C₃	C₅×#391	1	1	yes	characteristic
193	C₂×C₃	C₅×#416	1	2	yes	—
194	C₂×C₃	C₅×#488	1	2	yes	—
195	C₂×C₃	C₅×#499	1	2	yes	—
196	C₅	C₃×#1991	1	1	yes	characteristic, direct product factor, Sylow
197	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²	C₃×C₅×#124	1	1	yes	characteristic
199	C₂²	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
200	C₂²	C₃×C₅×#135	1	4	yes	—
201	C₄	—	2	4	no	—
202	C₄	—	4	4	no	—
203	C₄	—	8	2	no	—
204	C₄	C₃×C₄×C₅×Q₈	1	2	yes	—
205	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
206	C₃	C₅×#1991	1	1	yes	characteristic, direct product factor, Sylow
207	C₂	C₃×C₅×#391	1	1	yes	characteristic
208	C₂	C₃×C₅×#416	1	2	yes	—
209	C₂	C₃×C₅×#488	1	2	yes	—
210	C₂	C₃×C₅×#499	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
5. C₅×#1991	C₃	direct (N × H)
8. C₃×C₅×#125	C₄	semidirect
15. C₃×#1991	C₅	direct (N × H)
39. C₅×#125	C₃×C₄	semidirect
46. #1991	C₃×C₅	direct (N × H)
61. C₃×#125	C₄×C₅	semidirect
121. #125	C₃×C₄×C₅	semidirect
166. C₃×C₅	#1991	direct (N × H)
196. C₅	C₃×#1991	direct (N × H)
206. C₃	C₅×#1991	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×#125	2
C₂×C₃×C₄×C₅×C₈	2
C₃×C₅×#382	2
C₃×C₅×#340	2
C₅×#1991	3
C₃×#1991	5

Subgroups — C3×C5×#1991 #14275025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1991 #14275025