Subgroups — C₃×C₅×#1695 #14274729

Order 1920.

308 conjugacy classes of subgroups.

The subgroup lattice has 236 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×#436	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#333	C₂	1	2	yes	maximal, complemented
6	C₅×#1695	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×M₁₆	—	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×#1695	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×#436	C₂×C₃	1	1	yes	characteristic
22	C₅×#334	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	C₃×C₅×M₁₆	—	4	2	no	—
28	C₂×C₃×C₅×C₈	—	2	1	no	—
29	C₂×C₃×C₅×C₈	—	2	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×#436	C₂×C₅	1	1	yes	characteristic
40	C₃×#334	C₂×C₅	1	1	yes	characteristic, complemented
41	C₃×#333	C₂×C₅	1	2	yes	complemented
42	C₂×C₅×M₁₆	—	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	#1695	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	2	no	—
57	C₂×C₃×C₄×C₅	—	2	1	no	—
58	C₂×C₃×C₄×C₅	—	4	1	no	—
59	C₂×C₃×C₄×C₅	—	4	1	no	—
60	C₂×C₃×C₄×C₅	—	4	2	no	—
61	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
64	C₃×C₅×C₈	—	2	1	no	—
65	C₃×C₅×C₈	—	4	1	no	—
66	C₃×C₅×C₈	—	4	2	no	—
67	C₃×C₅×C₈	SD₁₆	1	2	yes	—
68	C₂×C₃×M₁₆	—	2	1	no	—
69	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
70	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
71	C₃×#107	—	2	1	no	—
72	C₃×#107	—	2	1	no	—
73	C₃×#106	—	2	2	no	—
74	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
75	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
76	C₃×#102	—	2	2	no	—
77	C₃×C₂²⋊C₈	—	2	1	no	—
78	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
79	C₂×C₅×Q₈	—	2	2	no	—
80	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	—	2	1	no	—
82	C₅×M₁₆	—	4	2	no	—
83	C₂×C₅×C₈	—	2	1	no	—
84	C₂×C₅×C₈	—	2	2	no	—
85	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
86	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
87	C₅×C₄⋊C₄	—	2	2	no	—
88	C₅×C₄⋊C₄	—	2	2	no	—
89	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
90	C₅×C₂²⋊C₄	—	2	1	no	—
91	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
92	#500	C₂×C₃×C₅	1	1	yes	characteristic, complemented
93	#476	C₂×C₃×C₅	1	2	yes	—
94	#436	C₂×C₃×C₅	1	1	yes	characteristic
95	#334	C₂×C₃×C₅	1	1	yes	characteristic, complemented
96	#333	C₂×C₃×C₅	1	2	yes	complemented
97	C₂²×C₃×C₅	—	4	1	no	—
98	C₂²×C₃×C₅	—	4	1	no	—
99	C₂²×C₃×C₅	—	4	1	no	—
100	C₂²×C₃×C₅	#121	1	1	yes	characteristic
101	C₃×C₄×C₅	—	2	1	no	—
102	C₃×C₄×C₅	—	4	1	no	—
103	C₃×C₄×C₅	—	8	2	no	—
104	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
105	C₃×C₄×C₅	#137	1	1	yes	characteristic
106	C₃×C₄×C₅	#137	1	2	yes	—
107	C₂×C₃×Q₈	—	2	2	no	—
108	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
109	C₂²×C₃×C₄	—	2	1	no	—
110	C₃×M₁₆	—	4	2	no	—
111	C₂×C₃×C₈	—	2	1	no	—
112	C₂×C₃×C₈	—	2	2	no	—
113	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
114	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
115	C₃×C₄⋊C₄	—	2	2	no	—
116	C₃×C₄⋊C₄	—	2	2	no	—
117	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
118	C₃×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
120	C₂³×C₅	—	2	1	no	—
121	C₅×Q₈	—	8	2	no	—
122	C₅×D₄	—	2	2	no	—
123	C₂×C₄×C₅	—	2	1	no	—
124	C₂×C₄×C₅	—	4	1	no	—
125	C₂×C₄×C₅	—	4	1	no	—
126	C₂×C₄×C₅	—	4	2	no	—
127	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
128	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
129	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
130	C₅×C₈	—	2	1	no	—
131	C₅×C₈	—	4	1	no	—
132	C₅×C₈	—	4	2	no	—
133	C₅×C₈	C₃×SD₁₆	1	2	yes	—
134	C₂×M₁₆	—	2	1	no	—
135	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
136	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
137	#107	—	2	1	no	—
138	#107	—	2	1	no	—
139	#106	—	2	2	no	—
140	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
141	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
142	#102	—	2	2	no	—
143	C₂²⋊C₈	—	2	1	no	—
144	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
145	C₂×C₃×C₅	—	8	1	no	—
146	C₂×C₃×C₅	#461	1	1	yes	characteristic
147	C₂×C₃×C₅	#470	1	1	yes	characteristic
148	C₂×C₃×C₅	#472	1	1	yes	characteristic
149	C₂³×C₃	—	2	1	no	—
150	C₃×Q₈	—	8	2	no	—
151	C₃×D₄	—	2	2	no	—
152	C₂×C₃×C₄	—	2	1	no	—
153	C₂×C₃×C₄	—	4	1	no	—
154	C₂×C₃×C₄	—	4	1	no	—
155	C₂×C₃×C₄	—	4	2	no	—
156	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
159	C₃×C₈	—	2	1	no	—
160	C₃×C₈	—	4	1	no	—
161	C₃×C₈	—	4	2	no	—
162	C₃×C₈	C₅×SD₁₆	1	2	yes	—
163	C₂²×C₅	—	4	1	no	—
164	C₂²×C₅	—	4	1	no	—
165	C₂²×C₅	—	4	1	no	—
166	C₂²×C₅	C₃×#121	1	1	yes	characteristic
167	C₄×C₅	—	2	1	no	—
168	C₄×C₅	—	4	1	no	—
169	C₄×C₅	—	8	2	no	—
170	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
171	C₄×C₅	C₃×#137	1	1	yes	characteristic
172	C₄×C₅	C₃×#137	1	2	yes	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
175	C₂²×C₄	—	2	1	no	—
176	M₁₆	—	4	2	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
180	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
184	C₂²⋊C₄	—	2	1	no	—
185	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
186	C₃×C₅	#1695	1	1	yes	characteristic, direct product factor, Hall
187	C₂²×C₃	—	4	1	no	—
188	C₂²×C₃	—	4	1	no	—
189	C₂²×C₃	—	4	1	no	—
190	C₂²×C₃	C₅×#121	1	1	yes	characteristic
191	C₃×C₄	—	2	1	no	—
192	C₃×C₄	—	4	1	no	—
193	C₃×C₄	—	8	2	no	—
194	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
195	C₃×C₄	C₅×#137	1	1	yes	characteristic
196	C₃×C₄	C₅×#137	1	2	yes	—
197	C₂×C₅	—	8	1	no	—
198	C₂×C₅	C₃×#461	1	1	yes	characteristic
199	C₂×C₅	C₃×#470	1	1	yes	characteristic
200	C₂×C₅	C₃×#472	1	1	yes	characteristic
201	C₂³	—	2	1	no	—
202	Q₈	—	8	2	no	—
203	D₄	—	2	2	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
209	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
210	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
211	C₈	—	2	1	no	—
212	C₈	—	4	1	no	—
213	C₈	—	4	2	no	—
214	C₈	C₃×C₅×SD₁₆	1	2	yes	—
215	C₂×C₃	—	8	1	no	—
216	C₂×C₃	C₅×#461	1	1	yes	characteristic
217	C₂×C₃	C₅×#470	1	1	yes	characteristic
218	C₂×C₃	C₅×#472	1	1	yes	characteristic
219	C₅	C₃×#1695	1	1	yes	characteristic, direct product factor, Sylow
220	C₂²	—	4	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	4	1	no	—
223	C₂²	C₃×C₅×#121	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	4	1	no	—
226	C₄	—	8	2	no	—
227	C₄	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
228	C₄	C₃×C₅×#137	1	1	yes	characteristic
229	C₄	C₃×C₅×#137	1	2	yes	—
230	C₃	C₅×#1695	1	1	yes	characteristic, direct product factor, Sylow
231	C₂	—	8	1	no	—
232	C₂	C₃×C₅×#461	1	1	yes	characteristic
233	C₂	C₃×C₅×#470	1	1	yes	characteristic
234	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×#334	C₂	semidirect
5. C₃×C₅×#333	C₂	semidirect
6. C₅×#1695	C₃	direct (N × H)
18. C₃×#1695	C₅	direct (N × H)
19. C₅×#500	C₂×C₃	semidirect
22. C₅×#334	C₂×C₃	semidirect
23. C₅×#333	C₂×C₃	semidirect
37. C₃×#500	C₂×C₅	semidirect
40. C₃×#334	C₂×C₅	semidirect
41. C₃×#333	C₂×C₅	semidirect
53. #1695	C₃×C₅	direct (N × H)
92. #500	C₂×C₃×C₅	semidirect
95. #334	C₂×C₃×C₅	semidirect
96. #333	C₂×C₃×C₅	semidirect
186. C₃×C₅	#1695	direct (N × H)
219. C₅	C₃×#1695	direct (N × H)
230. C₃	C₅×#1695	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×#436	2
C₃×C₅×#334	2
C₃×C₅×#333	2
C₅×#1695	3
C₃×#1695	5

Subgroups — C3×C5×#1695 #14274729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1695 #14274729