Subgroups — C₃×C₅×#2103 #14275137

Order 1920.

296 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#430	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#344	C₂	1	2	yes	maximal
4	C₃×C₅×#341	C₂	1	2	yes	maximal
5	C₃×C₅×#338	C₂	1	1	yes	maximal, characteristic
6	C₅×#2103	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
8	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
9	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₂²	1	1	yes	characteristic
12	C₃×C₅×#108	—	2	2	no	—
13	C₃×C₅×C₄⋊C₈	—	2	2	no	—
14	C₃×#2103	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×#430	C₂×C₃	1	1	yes	characteristic
16	C₅×#424	C₂×C₃	1	1	yes	characteristic
17	C₅×#344	C₂×C₃	1	2	yes	—
18	C₅×#341	C₂×C₃	1	2	yes	—
19	C₅×#338	C₂×C₃	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
21	C₃×C₅×M₁₆	—	2	2	no	—
22	C₃×C₅×M₁₆	—	2	2	no	—
23	C₃×C₅×M₁₆	—	2	2	no	—
24	C₃×C₅×M₁₆	—	2	2	no	—
25	C₃×C₅×M₁₆	—	2	2	no	—
26	C₂×C₃×C₅×C₈	—	2	1	no	—
27	C₂×C₃×C₅×C₈	—	2	2	no	—
28	C₂×C₃×C₅×C₈	—	2	2	no	—
29	C₂×C₃×C₅×C₈	—	2	2	no	—
30	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
31	C₃×C₅×C₄⋊C₄	—	2	1	no	—
32	C₃×C₅×C₂²⋊C₄	Q₈	1	2	yes	—
33	C₃×C₄²×C₅	—	2	1	no	—
34	C₃×#430	C₂×C₅	1	1	yes	characteristic
35	C₃×#424	C₂×C₅	1	1	yes	characteristic
36	C₃×#344	C₂×C₅	1	2	yes	—
37	C₃×#341	C₂×C₅	1	2	yes	—
38	C₃×#338	C₂×C₅	1	1	yes	characteristic
39	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
40	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
41	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
42	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
43	C₅×#117	C₂²×C₃	1	1	yes	characteristic
44	C₅×#108	—	2	2	no	—
45	C₅×C₄⋊C₈	—	2	2	no	—
46	#2103	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
47	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₃×C₄×C₅	—	2	2	no	—
49	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	#41	1	2	yes	—
51	C₂×C₃×C₄×C₅	#41	1	2	yes	—
52	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
53	C₃×C₅×C₈	—	2	2	no	—
54	C₃×C₅×C₈	—	4	1	no	—
55	C₃×C₅×C₈	—	4	2	no	—
56	C₃×C₅×C₈	—	4	2	no	—
57	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
58	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
59	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
60	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
61	C₃×#117	C₂²×C₅	1	1	yes	characteristic
62	C₃×#108	—	2	2	no	—
63	C₃×C₄⋊C₈	—	2	2	no	—
64	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
65	C₅×M₁₆	—	2	2	no	—
66	C₅×M₁₆	—	2	2	no	—
67	C₅×M₁₆	—	2	2	no	—
68	C₅×M₁₆	—	2	2	no	—
69	C₅×M₁₆	—	2	2	no	—
70	C₂×C₅×C₈	—	2	1	no	—
71	C₂×C₅×C₈	—	2	2	no	—
72	C₂×C₅×C₈	—	2	2	no	—
73	C₂×C₅×C₈	—	2	2	no	—
74	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
75	C₅×C₄⋊C₄	—	2	1	no	—
76	C₅×C₂²⋊C₄	C₃×Q₈	1	2	yes	—
77	C₄²×C₅	—	2	1	no	—
78	#430	C₂×C₃×C₅	1	1	yes	characteristic
79	#424	C₂×C₃×C₅	1	1	yes	characteristic
80	#344	C₂×C₃×C₅	1	2	yes	—
81	#341	C₂×C₃×C₅	1	2	yes	—
82	#338	C₂×C₃×C₅	1	1	yes	characteristic
83	C₂²×C₃×C₅	—	4	1	no	—
84	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂²×C₃×C₅	#125	1	2	yes	—
86	C₃×C₄×C₅	—	4	2	no	—
87	C₃×C₄×C₅	#123	1	1	yes	characteristic
88	C₃×C₄×C₅	#124	1	1	yes	characteristic
89	C₃×C₄×C₅	#126	1	2	yes	—
90	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
91	C₃×M₁₆	—	2	2	no	—
92	C₃×M₁₆	—	2	2	no	—
93	C₃×M₁₆	—	2	2	no	—
94	C₃×M₁₆	—	2	2	no	—
95	C₃×M₁₆	—	2	2	no	—
96	C₂×C₃×C₈	—	2	1	no	—
97	C₂×C₃×C₈	—	2	2	no	—
98	C₂×C₃×C₈	—	2	2	no	—
99	C₂×C₃×C₈	—	2	2	no	—
100	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
101	C₃×C₄⋊C₄	—	2	1	no	—
102	C₃×C₂²⋊C₄	C₅×Q₈	1	2	yes	—
103	C₃×C₄²	—	2	1	no	—
104	C₂³×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
105	C₂×C₄×C₅	—	2	2	no	—
106	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
107	C₂×C₄×C₅	C₃×#41	1	2	yes	—
108	C₂×C₄×C₅	C₃×#41	1	2	yes	—
109	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
110	C₅×C₈	—	2	2	no	—
111	C₅×C₈	—	4	1	no	—
112	C₅×C₈	—	4	2	no	—
113	C₅×C₈	—	4	2	no	—
114	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
115	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
116	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
117	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
118	#117	C₂²×C₃×C₅	1	1	yes	characteristic
119	#108	—	2	2	no	—
120	C₄⋊C₈	—	2	2	no	—
121	C₂×C₃×C₅	—	2	1	no	—
122	C₂×C₃×C₅	—	2	2	no	—
123	C₂×C₃×C₅	#400	1	1	yes	characteristic
124	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
125	C₂×C₃×C₄	—	2	2	no	—
126	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄	C₅×#41	1	2	yes	—
128	C₂×C₃×C₄	C₅×#41	1	2	yes	—
129	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
130	C₃×C₈	—	2	2	no	—
131	C₃×C₈	—	4	1	no	—
132	C₃×C₈	—	4	2	no	—
133	C₃×C₈	—	4	2	no	—
134	C₂²×C₅	—	4	1	no	—
135	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
136	C₂²×C₅	C₃×#125	1	2	yes	—
137	C₄×C₅	—	4	2	no	—
138	C₄×C₅	C₃×#123	1	1	yes	characteristic
139	C₄×C₅	C₃×#124	1	1	yes	characteristic
140	C₄×C₅	C₃×#126	1	2	yes	—
141	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
142	M₁₆	—	2	2	no	—
143	M₁₆	—	2	2	no	—
144	M₁₆	—	2	2	no	—
145	M₁₆	—	2	2	no	—
146	M₁₆	—	2	2	no	—
147	C₂×C₈	—	2	1	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
152	C₄⋊C₄	—	2	1	no	—
153	C₂²⋊C₄	C₃×C₅×Q₈	1	2	yes	—
154	C₄²	—	2	1	no	—
155	C₃×C₅	#2103	1	1	yes	characteristic, direct product factor, Hall
156	C₂²×C₃	—	4	1	no	—
157	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
158	C₂²×C₃	C₅×#125	1	2	yes	—
159	C₃×C₄	—	4	2	no	—
160	C₃×C₄	C₅×#123	1	1	yes	characteristic
161	C₃×C₄	C₅×#124	1	1	yes	characteristic
162	C₃×C₄	C₅×#126	1	2	yes	—
163	C₂×C₅	—	2	1	no	—
164	C₂×C₅	—	2	2	no	—
165	C₂×C₅	C₃×#400	1	1	yes	characteristic
166	C₂³	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
169	C₂×C₄	C₃×C₅×#41	1	2	yes	—
170	C₂×C₄	C₃×C₅×#41	1	2	yes	—
171	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
172	C₈	—	2	2	no	—
173	C₈	—	4	1	no	—
174	C₈	—	4	2	no	—
175	C₈	—	4	2	no	—
176	C₂×C₃	—	2	1	no	—
177	C₂×C₃	—	2	2	no	—
178	C₂×C₃	C₅×#400	1	1	yes	characteristic
179	C₅	C₃×#2103	1	1	yes	characteristic, direct product factor, Sylow
180	C₂²	—	4	1	no	—
181	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
182	C₂²	C₃×C₅×#125	1	2	yes	—
183	C₄	—	4	2	no	—
184	C₄	C₃×C₅×#123	1	1	yes	characteristic
185	C₄	C₃×C₅×#124	1	1	yes	characteristic
186	C₄	C₃×C₅×#126	1	2	yes	—
187	C₃	C₅×#2103	1	1	yes	characteristic, direct product factor, Sylow
188	C₂	—	2	1	no	—
189	C₂	—	2	2	no	—
190	C₂	C₃×C₅×#400	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂×C₃×C₅	#400
prime radical	C₂³×C₃×C₅	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#2103	C₃	direct (N × H)
14. C₃×#2103	C₅	direct (N × H)
46. #2103	C₃×C₅	direct (N × H)
155. C₃×C₅	#2103	direct (N × H)
179. C₅	C₃×#2103	direct (N × H)
187. C₃	C₅×#2103	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×#430	2
C₃×C₅×#424	2
C₃×C₅×#344	2
C₃×C₅×#341	2
C₃×C₅×#338	2
C₅×#2103	3
C₃×#2103	5

Subgroups — C3×C5×#2103 #14275137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2103 #14275137