Subgroups — C₃×C₅×#1992 #14275026

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 232 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×C₅×#97	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#340	C₂	1	4	yes	maximal
5	C₅×#1992	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	—	2	2	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×#97	—	2	2	no	—
15	C₃×#1992	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic
17	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic
18	C₅×#384	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	—	4	4	no	—
31	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
32	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
33	C₃×C₄²×C₅	D₄	1	2	yes	—
34	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic
35	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic
36	C₃×#384	C₂×C₅	1	1	yes	characteristic
37	C₃×#340	C₂×C₅	1	4	yes	—
38	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
39	C₅×#125	—	2	2	no	—
40	C₅×#125	C₃×C₄	1	4	yes	complemented
41	C₂×C₅×C₄⋊C₄	—	2	2	no	—
42	C₂×C₅×C₄⋊C₄	—	2	2	no	—
43	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
44	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
45	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
46	C₅×#97	—	2	2	no	—
47	#1992	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
48	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	—	2	2	no	—
50	C₂×C₃×C₄×C₅	—	2	2	no	—
51	C₂×C₃×C₄×C₅	—	2	4	no	—
52	C₂×C₃×C₄×C₅	—	4	2	no	—
53	C₂×C₃×C₄×C₅	—	4	2	no	—
54	C₂×C₃×C₄×C₅	—	4	2	no	—
55	C₂×C₃×C₄×C₅	—	4	4	no	—
56	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
57	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
60	C₂×C₃×C₄×C₅	#41	1	2	yes	—
61	C₃×C₅×C₈	—	2	4	no	—
62	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
63	C₃×#125	—	2	2	no	—
64	C₃×#125	C₄×C₅	1	4	yes	complemented
65	C₂×C₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
68	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
69	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
70	C₃×#97	—	2	2	no	—
71	C₂²×C₄×C₅	—	2	2	no	—
72	C₂²×C₄×C₅	—	2	2	no	—
73	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
74	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
75	C₂×C₅×C₈	—	2	2	no	—
76	C₂×C₅×C₈	—	2	2	no	—
77	C₂×C₅×C₈	C₃×Q₈	1	4	yes	—
78	C₅×C₄⋊C₄	—	2	8	no	—
79	C₅×C₄⋊C₄	—	2	2	no	—
80	C₅×C₄⋊C₄	—	2	4	no	—
81	C₅×C₄⋊C₄	—	4	4	no	—
82	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
83	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
84	C₄²×C₅	C₃×D₄	1	2	yes	—
85	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic
86	C₂×#97	C₂×C₃×C₅	1	1	yes	characteristic
87	#384	C₂×C₃×C₅	1	1	yes	characteristic
88	#340	C₂×C₃×C₅	1	4	yes	—
89	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₃×C₅	#124	1	1	yes	characteristic
91	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
92	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
93	C₂²×C₃×C₅	#137	1	2	yes	—
94	C₃×C₄×C₅	—	2	4	no	—
95	C₃×C₄×C₅	—	4	4	no	—
96	C₃×C₄×C₅	—	8	2	no	—
97	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
98	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
99	C₂²×C₃×C₄	—	2	2	no	—
100	C₂²×C₃×C₄	—	2	2	no	—
101	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
102	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
103	C₂×C₃×C₈	—	2	2	no	—
104	C₂×C₃×C₈	—	2	2	no	—
105	C₂×C₃×C₈	C₅×Q₈	1	4	yes	—
106	C₃×C₄⋊C₄	—	2	8	no	—
107	C₃×C₄⋊C₄	—	2	2	no	—
108	C₃×C₄⋊C₄	—	2	4	no	—
109	C₃×C₄⋊C₄	—	4	4	no	—
110	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
111	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
112	C₃×C₄²	C₅×D₄	1	2	yes	—
113	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
114	C₂×C₄×C₅	—	2	2	no	—
115	C₂×C₄×C₅	—	2	2	no	—
116	C₂×C₄×C₅	—	2	4	no	—
117	C₂×C₄×C₅	—	4	2	no	—
118	C₂×C₄×C₅	—	4	2	no	—
119	C₂×C₄×C₅	—	4	2	no	—
120	C₂×C₄×C₅	—	4	4	no	—
121	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
122	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
123	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
124	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
125	C₂×C₄×C₅	C₃×#41	1	2	yes	—
126	C₅×C₈	—	2	4	no	—
127	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
128	#125	—	2	2	no	—
129	#125	C₃×C₄×C₅	1	4	yes	complemented
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
133	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
134	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
135	#97	—	2	2	no	—
136	C₂×C₃×C₅	#391	1	1	yes	characteristic
137	C₂×C₃×C₅	#417	1	2	yes	—
138	C₂×C₃×C₅	#490	1	1	yes	characteristic
139	C₂×C₃×C₅	#491	1	1	yes	characteristic
140	C₂×C₃×C₅	#501	1	2	yes	—
141	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄	—	2	2	no	—
143	C₂×C₃×C₄	—	2	2	no	—
144	C₂×C₃×C₄	—	2	4	no	—
145	C₂×C₃×C₄	—	4	2	no	—
146	C₂×C₃×C₄	—	4	2	no	—
147	C₂×C₃×C₄	—	4	2	no	—
148	C₂×C₃×C₄	—	4	4	no	—
149	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
150	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
151	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
153	C₂×C₃×C₄	C₅×#41	1	2	yes	—
154	C₃×C₈	—	2	4	no	—
155	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₅	C₃×#124	1	1	yes	characteristic
157	C₂²×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
158	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
159	C₂²×C₅	C₃×#137	1	2	yes	—
160	C₄×C₅	—	2	4	no	—
161	C₄×C₅	—	4	4	no	—
162	C₄×C₅	—	8	2	no	—
163	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
164	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
168	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	C₃×C₅×Q₈	1	4	yes	—
172	C₄⋊C₄	—	2	8	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	4	4	no	—
176	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
177	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
178	C₄²	C₃×C₅×D₄	1	2	yes	—
179	C₃×C₅	#1992	1	1	yes	characteristic, direct product factor, Hall
180	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₃	C₅×#124	1	1	yes	characteristic
182	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
183	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
184	C₂²×C₃	C₅×#137	1	2	yes	—
185	C₃×C₄	—	2	4	no	—
186	C₃×C₄	—	4	4	no	—
187	C₃×C₄	—	8	2	no	—
188	C₃×C₄	C₄×C₅×Q₈	1	2	yes	—
189	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
190	C₂×C₅	C₃×#391	1	1	yes	characteristic
191	C₂×C₅	C₃×#417	1	2	yes	—
192	C₂×C₅	C₃×#490	1	1	yes	characteristic
193	C₂×C₅	C₃×#491	1	1	yes	characteristic
194	C₂×C₅	C₃×#501	1	2	yes	—
195	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	4	yes	—
204	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
206	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
207	C₂×C₄	C₃×C₅×#41	1	2	yes	—
208	C₈	—	2	4	no	—
209	C₂×C₃	C₅×#391	1	1	yes	characteristic
210	C₂×C₃	C₅×#417	1	2	yes	—
211	C₂×C₃	C₅×#490	1	1	yes	characteristic
212	C₂×C₃	C₅×#491	1	1	yes	characteristic
213	C₂×C₃	C₅×#501	1	2	yes	—
214	C₅	C₃×#1992	1	1	yes	characteristic, direct product factor, Sylow
215	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²	C₃×C₅×#124	1	1	yes	characteristic
217	C₂²	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
218	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
219	C₂²	C₃×C₅×#137	1	2	yes	—
220	C₄	—	2	4	no	—
221	C₄	—	4	4	no	—
222	C₄	—	8	2	no	—
223	C₄	C₃×C₄×C₅×Q₈	1	2	yes	—
224	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
225	C₃	C₅×#1992	1	1	yes	characteristic, direct product factor, Sylow
226	C₂	C₃×C₅×#391	1	1	yes	characteristic
227	C₂	C₃×C₅×#417	1	2	yes	—
228	C₂	C₃×C₅×#490	1	1	yes	characteristic
229	C₂	C₃×C₅×#491	1	1	yes	characteristic
230	C₂	C₃×C₅×#501	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×#1992	C₃	direct (N × H)
8. C₃×C₅×#125	C₄	semidirect
15. C₃×#1992	C₅	direct (N × H)
40. C₅×#125	C₃×C₄	semidirect
47. #1992	C₃×C₅	direct (N × H)
64. C₃×#125	C₄×C₅	semidirect
129. #125	C₃×C₄×C₅	semidirect
179. C₃×C₅	#1992	direct (N × H)
214. C₅	C₃×#1992	direct (N × H)
225. C₃	C₅×#1992	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×C₅×#97	2
C₃×C₅×#384	2
C₃×C₅×#340	2
C₅×#1992	3
C₃×#1992	5

Subgroups — C3×C5×#1992 #14275026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1992 #14275026