Subgroups — C₃×C₅×#1846 #14274880

Order 1920.

496 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	C₂×C₃×C₅×#107	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×#106	C₂	1	2	yes	maximal
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#382	C₂	1	2	yes	maximal
5	C₅×#1846	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×#107	—	2	4	no	—
11	C₃×C₅×#106	—	2	4	no	—
12	C₃×C₄×C₅×C₈	C₄	1	4	yes	complemented
13	C₃×C₅×#95	—	2	4	no	—
14	C₃×#1846	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×#107	C₂×C₃	1	2	yes	—
16	C₂×C₅×#106	C₂×C₃	1	2	yes	—
17	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
18	C₅×#382	C₂×C₃	1	2	yes	—
19	C₂²×C₃×C₄×C₅	—	2	4	no	—
20	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
21	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
24	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
25	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
26	C₂×C₃×C₅×C₈	Q₈	1	2	yes	—
27	C₂×C₃×C₅×C₈	Q₈	1	2	yes	—
28	C₃×C₅×C₄⋊C₄	—	2	4	no	—
29	C₃×C₅×C₄⋊C₄	—	2	4	no	—
30	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
31	C₃×C₄²×C₅	Q₈	1	2	yes	—
32	C₂×C₃×#107	C₂×C₅	1	2	yes	—
33	C₂×C₃×#106	C₂×C₅	1	2	yes	—
34	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
35	C₃×#382	C₂×C₅	1	2	yes	—
36	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
37	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
39	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
40	C₅×#107	—	2	4	no	—
41	C₅×#106	—	2	4	no	—
42	C₄×C₅×C₈	C₃×C₄	1	4	yes	complemented
43	C₅×#95	—	2	4	no	—
44	#1846	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₅	—	2	4	no	—
47	C₂×C₃×C₄×C₅	—	4	4	no	—
48	C₂×C₃×C₄×C₅	—	4	8	no	—
49	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
50	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
52	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
56	C₃×C₅×C₈	C₄⋊C₄	1	4	yes	—
57	C₃×C₅×C₈	C₄⋊C₄	1	4	yes	—
58	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
59	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
60	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
61	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
62	C₃×#107	—	2	4	no	—
63	C₃×#106	—	2	4	no	—
64	C₃×C₄×C₈	C₄×C₅	1	4	yes	complemented
65	C₃×#95	—	2	4	no	—
66	C₂²×C₄×C₅	—	2	4	no	—
67	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
68	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
69	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
70	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
71	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
72	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
73	C₂×C₅×C₈	C₃×Q₈	1	2	yes	—
74	C₂×C₅×C₈	C₃×Q₈	1	2	yes	—
75	C₅×C₄⋊C₄	—	2	4	no	—
76	C₅×C₄⋊C₄	—	2	4	no	—
77	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
78	C₄²×C₅	C₃×Q₈	1	2	yes	—
79	C₂×#107	C₂×C₃×C₅	1	2	yes	—
80	C₂×#106	C₂×C₃×C₅	1	2	yes	—
81	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic
82	#382	C₂×C₃×C₅	1	2	yes	—
83	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₃×C₅	#127	1	1	yes	characteristic
85	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
86	C₂²×C₃×C₅	#135	1	4	yes	—
87	C₃×C₄×C₅	—	2	4	no	—
88	C₃×C₄×C₅	—	8	4	no	—
89	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
92	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
93	C₂²×C₃×C₄	—	2	4	no	—
94	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
95	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
96	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
97	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
98	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
99	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
100	C₂×C₃×C₈	C₅×Q₈	1	2	yes	—
101	C₂×C₃×C₈	C₅×Q₈	1	2	yes	—
102	C₃×C₄⋊C₄	—	2	4	no	—
103	C₃×C₄⋊C₄	—	2	4	no	—
104	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
105	C₃×C₄²	C₅×Q₈	1	2	yes	—
106	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
107	C₂×C₄×C₅	—	2	4	no	—
108	C₂×C₄×C₅	—	4	4	no	—
109	C₂×C₄×C₅	—	4	8	no	—
110	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
111	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
112	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
113	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
114	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
115	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
116	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
117	C₅×C₈	C₃×C₄⋊C₄	1	4	yes	—
118	C₅×C₈	C₃×C₄⋊C₄	1	4	yes	—
119	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
120	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
121	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
122	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
123	#107	—	2	4	no	—
124	#106	—	2	4	no	—
125	C₄×C₈	C₃×C₄×C₅	1	4	yes	complemented
126	#95	—	2	4	no	—
127	C₂×C₃×C₅	#384	1	1	yes	characteristic
128	C₂×C₃×C₅	#427	1	2	yes	—
129	C₂×C₃×C₅	#495	1	2	yes	—
130	C₂×C₃×C₅	#499	1	2	yes	—
131	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
132	C₂×C₃×C₄	—	2	4	no	—
133	C₂×C₃×C₄	—	4	4	no	—
134	C₂×C₃×C₄	—	4	8	no	—
135	C₂×C₃×C₄	C₅×C₄⋊C₄	1	4	yes	—
136	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
137	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
140	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
141	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
142	C₃×C₈	C₅×C₄⋊C₄	1	4	yes	—
143	C₃×C₈	C₅×C₄⋊C₄	1	4	yes	—
144	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
145	C₂²×C₅	C₃×#127	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	—	8	4	no	—
150	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
151	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
152	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
153	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
156	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
157	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
158	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
159	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
160	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
161	C₂×C₈	C₃×C₅×Q₈	1	2	yes	—
162	C₂×C₈	C₃×C₅×Q₈	1	2	yes	—
163	C₄⋊C₄	—	2	4	no	—
164	C₄⋊C₄	—	2	4	no	—
165	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
166	C₄²	C₃×C₅×Q₈	1	2	yes	—
167	C₃×C₅	#1846	1	1	yes	characteristic, direct product factor, Hall
168	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₃	C₅×#127	1	1	yes	characteristic
170	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
171	C₂²×C₃	C₅×#135	1	4	yes	—
172	C₃×C₄	—	2	4	no	—
173	C₃×C₄	—	8	4	no	—
174	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
175	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
176	C₃×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
177	C₃×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
178	C₂×C₅	C₃×#384	1	1	yes	characteristic
179	C₂×C₅	C₃×#427	1	2	yes	—
180	C₂×C₅	C₃×#495	1	2	yes	—
181	C₂×C₅	C₃×#499	1	2	yes	—
182	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	8	no	—
186	C₂×C₄	C₃×C₅×C₄⋊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×D₄	1	1	yes	characteristic
190	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
191	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
192	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
193	C₈	C₃×C₅×C₄⋊C₄	1	4	yes	—
194	C₈	C₃×C₅×C₄⋊C₄	1	4	yes	—
195	C₂×C₃	C₅×#384	1	1	yes	characteristic
196	C₂×C₃	C₅×#427	1	2	yes	—
197	C₂×C₃	C₅×#495	1	2	yes	—
198	C₂×C₃	C₅×#499	1	2	yes	—
199	C₅	C₃×#1846	1	1	yes	characteristic, direct product factor, Sylow
200	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
201	C₂²	C₃×C₅×#127	1	1	yes	characteristic
202	C₂²	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
203	C₂²	C₃×C₅×#135	1	4	yes	—
204	C₄	—	2	4	no	—
205	C₄	—	8	4	no	—
206	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
207	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
208	C₄	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
209	C₄	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
210	C₃	C₅×#1846	1	1	yes	characteristic, direct product factor, Sylow
211	C₂	C₃×C₅×#384	1	1	yes	characteristic
212	C₂	C₃×C₅×#427	1	2	yes	—
213	C₂	C₃×C₅×#495	1	2	yes	—
214	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×#1846	C₃	direct (N × H)
12. C₃×C₄×C₅×C₈	C₄	semidirect
14. C₃×#1846	C₅	direct (N × H)
42. C₄×C₅×C₈	C₃×C₄	semidirect
44. #1846	C₃×C₅	direct (N × H)
64. C₃×C₄×C₈	C₄×C₅	semidirect
125. C₄×C₈	C₃×C₄×C₅	semidirect
167. C₃×C₅	#1846	direct (N × H)
199. C₅	C₃×#1846	direct (N × H)
210. C₃	C₅×#1846	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×#107	2
C₂×C₃×C₅×#106	2
C₂×C₃×C₄×C₅×C₈	2
C₃×C₅×#382	2
C₅×#1846	3
C₃×#1846	5

Subgroups — C3×C5×#1846 #14274880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1846 #14274880