Subgroups — C₃×C₅×#1675 #14274709

Order 1920.

320 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#476	C₂	1	2	yes	maximal
3	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#335	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#333	C₂	1	2	yes	maximal, complemented
6	C₅×#1675	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×C₈	—	2	1	no	—
8	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
9	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₃×C₅×#107	—	2	1	no	—
11	C₃×C₅×#107	—	2	1	no	—
12	C₃×C₅×#106	—	2	2	no	—
13	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#102	—	2	2	no	—
16	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
17	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×#1675	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₅×#500	C₂×C₃	1	1	yes	characteristic, complemented
20	C₅×#476	C₂×C₃	1	2	yes	—
21	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic
22	C₅×#335	C₂×C₃	1	1	yes	characteristic, complemented
23	C₅×#333	C₂×C₃	1	2	yes	complemented
24	C₂×C₃×C₅×Q₈	—	2	2	no	—
25	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	—	2	1	no	—
27	C₂×C₃×C₅×C₈	—	2	1	no	—
28	C₂×C₃×C₅×C₈	—	2	2	no	—
29	C₂×C₃×C₅×C₈	—	4	2	no	—
30	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
31	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₄	—	2	2	no	—
33	C₃×C₅×C₄⋊C₄	—	2	2	no	—
34	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
35	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
36	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
37	C₃×#500	C₂×C₅	1	1	yes	characteristic, complemented
38	C₃×#476	C₂×C₅	1	2	yes	—
39	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic
40	C₃×#335	C₂×C₅	1	1	yes	characteristic, complemented
41	C₃×#333	C₂×C₅	1	2	yes	complemented
42	C₂²×C₅×C₈	—	2	1	no	—
43	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
44	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
45	C₅×#107	—	2	1	no	—
46	C₅×#107	—	2	1	no	—
47	C₅×#106	—	2	2	no	—
48	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
49	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
50	C₅×#102	—	2	2	no	—
51	C₅×C₂²⋊C₈	—	2	1	no	—
52	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
53	#1675	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
54	C₂³×C₃×C₅	—	2	1	no	—
55	C₃×C₅×Q₈	—	8	2	no	—
56	C₃×C₅×D₄	—	2	1	no	—
57	C₃×C₅×D₄	Q₁₆	1	2	yes	—
58	C₂×C₃×C₄×C₅	—	2	1	no	—
59	C₂×C₃×C₄×C₅	—	4	1	no	—
60	C₂×C₃×C₄×C₅	—	4	1	no	—
61	C₂×C₃×C₄×C₅	—	4	2	no	—
62	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
64	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
65	C₃×C₅×C₈	—	2	1	no	—
66	C₃×C₅×C₈	—	4	1	no	—
67	C₃×C₅×C₈	—	4	2	no	—
68	C₃×C₅×C₈	SD₁₆	1	2	yes	—
69	C₂²×C₃×C₈	—	2	1	no	—
70	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
71	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
72	C₃×#107	—	2	1	no	—
73	C₃×#107	—	2	1	no	—
74	C₃×#106	—	2	2	no	—
75	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
76	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
77	C₃×#102	—	2	2	no	—
78	C₃×C₂²⋊C₈	—	2	1	no	—
79	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
80	C₂×C₅×Q₈	—	2	2	no	—
81	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	—	2	1	no	—
83	C₂×C₅×C₈	—	2	1	no	—
84	C₂×C₅×C₈	—	2	2	no	—
85	C₂×C₅×C₈	—	4	2	no	—
86	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
87	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
88	C₅×C₄⋊C₄	—	2	2	no	—
89	C₅×C₄⋊C₄	—	2	2	no	—
90	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
91	C₅×C₂²⋊C₄	—	2	1	no	—
92	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
93	#500	C₂×C₃×C₅	1	1	yes	characteristic, complemented
94	#476	C₂×C₃×C₅	1	2	yes	—
95	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic
96	#335	C₂×C₃×C₅	1	1	yes	characteristic, complemented
97	#333	C₂×C₃×C₅	1	2	yes	complemented
98	C₂²×C₃×C₅	—	2	2	no	—
99	C₂²×C₃×C₅	—	4	1	no	—
100	C₂²×C₃×C₅	—	4	1	no	—
101	C₂²×C₃×C₅	#121	1	1	yes	characteristic
102	C₃×C₄×C₅	—	2	1	no	—
103	C₃×C₄×C₅	—	4	1	no	—
104	C₃×C₄×C₅	—	8	2	no	—
105	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
106	C₃×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
107	C₃×C₄×C₅	#135	1	1	yes	characteristic
108	C₃×C₄×C₅	#137	1	1	yes	characteristic
109	C₂×C₃×Q₈	—	2	2	no	—
110	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
111	C₂²×C₃×C₄	—	2	1	no	—
112	C₂×C₃×C₈	—	2	1	no	—
113	C₂×C₃×C₈	—	2	2	no	—
114	C₂×C₃×C₈	—	4	2	no	—
115	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
116	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
117	C₃×C₄⋊C₄	—	2	2	no	—
118	C₃×C₄⋊C₄	—	2	2	no	—
119	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
120	C₃×C₂²⋊C₄	—	2	1	no	—
121	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
122	C₂³×C₅	—	2	1	no	—
123	C₅×Q₈	—	8	2	no	—
124	C₅×D₄	—	2	1	no	—
125	C₅×D₄	C₃×Q₁₆	1	2	yes	—
126	C₂×C₄×C₅	—	2	1	no	—
127	C₂×C₄×C₅	—	4	1	no	—
128	C₂×C₄×C₅	—	4	1	no	—
129	C₂×C₄×C₅	—	4	2	no	—
130	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
131	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
132	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
133	C₅×C₈	—	2	1	no	—
134	C₅×C₈	—	4	1	no	—
135	C₅×C₈	—	4	2	no	—
136	C₅×C₈	C₃×SD₁₆	1	2	yes	—
137	C₂²×C₈	—	2	1	no	—
138	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
139	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
140	#107	—	2	1	no	—
141	#107	—	2	1	no	—
142	#106	—	2	2	no	—
143	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
144	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
145	#102	—	2	2	no	—
146	C₂²⋊C₈	—	2	1	no	—
147	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
148	C₂×C₃×C₅	—	4	2	no	—
149	C₂×C₃×C₅	#461	1	1	yes	characteristic
150	C₂×C₃×C₅	#467	1	1	yes	characteristic
151	C₂×C₃×C₅	#472	1	1	yes	characteristic
152	C₂³×C₃	—	2	1	no	—
153	C₃×Q₈	—	8	2	no	—
154	C₃×D₄	—	2	1	no	—
155	C₃×D₄	C₅×Q₁₆	1	2	yes	—
156	C₂×C₃×C₄	—	2	1	no	—
157	C₂×C₃×C₄	—	4	1	no	—
158	C₂×C₃×C₄	—	4	1	no	—
159	C₂×C₃×C₄	—	4	2	no	—
160	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
163	C₃×C₈	—	2	1	no	—
164	C₃×C₈	—	4	1	no	—
165	C₃×C₈	—	4	2	no	—
166	C₃×C₈	C₅×SD₁₆	1	2	yes	—
167	C₂²×C₅	—	2	2	no	—
168	C₂²×C₅	—	4	1	no	—
169	C₂²×C₅	—	4	1	no	—
170	C₂²×C₅	C₃×#121	1	1	yes	characteristic
171	C₄×C₅	—	2	1	no	—
172	C₄×C₅	—	4	1	no	—
173	C₄×C₅	—	8	2	no	—
174	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
175	C₄×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
176	C₄×C₅	C₃×#135	1	1	yes	characteristic
177	C₄×C₅	C₃×#137	1	1	yes	characteristic
178	C₂×Q₈	—	2	2	no	—
179	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
180	C₂²×C₄	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
185	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
189	C₂²⋊C₄	—	2	1	no	—
190	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
191	C₃×C₅	#1675	1	1	yes	characteristic, direct product factor, Hall
192	C₂²×C₃	—	2	2	no	—
193	C₂²×C₃	—	4	1	no	—
194	C₂²×C₃	—	4	1	no	—
195	C₂²×C₃	C₅×#121	1	1	yes	characteristic
196	C₃×C₄	—	2	1	no	—
197	C₃×C₄	—	4	1	no	—
198	C₃×C₄	—	8	2	no	—
199	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
200	C₃×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
201	C₃×C₄	C₅×#135	1	1	yes	characteristic
202	C₃×C₄	C₅×#137	1	1	yes	characteristic
203	C₂×C₅	—	4	2	no	—
204	C₂×C₅	C₃×#461	1	1	yes	characteristic
205	C₂×C₅	C₃×#467	1	1	yes	characteristic
206	C₂×C₅	C₃×#472	1	1	yes	characteristic
207	C₂³	—	2	1	no	—
208	Q₈	—	8	2	no	—
209	D₄	—	2	1	no	—
210	D₄	C₃×C₅×Q₁₆	1	2	yes	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
216	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
217	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
218	C₈	—	2	1	no	—
219	C₈	—	4	1	no	—
220	C₈	—	4	2	no	—
221	C₈	C₃×C₅×SD₁₆	1	2	yes	—
222	C₂×C₃	—	4	2	no	—
223	C₂×C₃	C₅×#461	1	1	yes	characteristic
224	C₂×C₃	C₅×#467	1	1	yes	characteristic
225	C₂×C₃	C₅×#472	1	1	yes	characteristic
226	C₅	C₃×#1675	1	1	yes	characteristic, direct product factor, Sylow
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	1	no	—
230	C₂²	C₃×C₅×#121	1	1	yes	characteristic
231	C₄	—	2	1	no	—
232	C₄	—	4	1	no	—
233	C₄	—	8	2	no	—
234	C₄	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
235	C₄	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
236	C₄	C₃×C₅×#135	1	1	yes	characteristic
237	C₄	C₃×C₅×#137	1	1	yes	characteristic
238	C₃	C₅×#1675	1	1	yes	characteristic, direct product factor, Sylow
239	C₂	—	4	2	no	—
240	C₂	C₃×C₅×#461	1	1	yes	characteristic
241	C₂	C₃×C₅×#467	1	1	yes	characteristic
242	C₂	C₃×C₅×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₃×C₅
prime radical	C₂×C₃×C₅×D₄	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#500	C₂	semidirect
4. C₃×C₅×#335	C₂	semidirect
5. C₃×C₅×#333	C₂	semidirect
6. C₅×#1675	C₃	direct (N × H)
18. C₃×#1675	C₅	direct (N × H)
19. C₅×#500	C₂×C₃	semidirect
22. C₅×#335	C₂×C₃	semidirect
23. C₅×#333	C₂×C₃	semidirect
37. C₃×#500	C₂×C₅	semidirect
40. C₃×#335	C₂×C₅	semidirect
41. C₃×#333	C₂×C₅	semidirect
53. #1675	C₃×C₅	direct (N × H)
93. #500	C₂×C₃×C₅	semidirect
96. #335	C₂×C₃×C₅	semidirect
97. #333	C₂×C₃×C₅	semidirect
191. C₃×C₅	#1675	direct (N × H)
226. C₅	C₃×#1675	direct (N × H)
238. C₃	C₅×#1675	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×#500	2
C₃×C₅×#476	2
C₃×C₅×C₈×D₄	2
C₃×C₅×#335	2
C₃×C₅×#333	2
C₅×#1675	3
C₃×#1675	5

Subgroups — C3×C5×#1675 #14274709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1675 #14274709