Subgroups — C₃×C₅×#1966 #14275000

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#101	C₂	1	4	yes	maximal
4	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₅×#1966	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
7	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
8	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
9	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₄	1	4	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊C₈	—	2	2	no	—
15	C₃×C₅×#101	—	2	8	no	—
16	C₃×C₅×#97	—	2	1	no	—
17	C₃×C₄×C₅×C₈	—	2	1	no	—
18	C₃×#1966	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
20	C₅×#423	C₂×C₃	1	1	yes	characteristic
21	C₂×C₅×#101	C₂×C₃	1	4	yes	—
22	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×C₅×Q₈	—	2	2	no	—
24	C₂×C₃×C₅×Q₈	—	2	2	no	—
25	C₂×C₃×C₅×Q₈	—	2	4	no	—
26	C₂×C₃×C₅×Q₈	—	2	4	no	—
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₃×C₅×M₁₆	—	2	2	no	—
31	C₃×C₅×M₁₆	—	2	4	no	—
32	C₃×C₅×M₁₆	D₄	1	4	yes	—
33	C₂×C₃×C₅×C₈	—	2	2	no	—
34	C₂×C₃×C₅×C₈	—	2	2	no	—
35	C₃×C₅×C₄⋊C₄	—	2	4	no	—
36	C₃×C₅×C₄⋊C₄	—	2	4	no	—
37	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
38	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
39	C₃×C₄²×C₅	D₄	1	2	yes	—
40	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
41	C₃×#423	C₂×C₅	1	1	yes	characteristic
42	C₂×C₃×#101	C₂×C₅	1	4	yes	—
43	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
44	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
45	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
46	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
47	C₅×C₄⋊Q₈	—	2	1	no	—
48	C₅×C₄⋊Q₈	—	2	1	no	—
49	C₅×C₄⋊Q₈	—	2	2	no	—
50	C₂×C₅×C₄⋊C₄	C₃×C₄	1	4	yes	—
51	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
52	C₅×C₄⋊C₈	—	2	2	no	—
53	C₅×#101	—	2	8	no	—
54	C₅×#97	—	2	1	no	—
55	C₄×C₅×C₈	—	2	1	no	—
56	#1966	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
57	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
58	C₃×C₅×Q₈	—	4	4	no	—
59	C₃×C₅×Q₈	—	4	2	no	—
60	C₃×C₅×Q₈	—	4	2	no	—
61	C₂×C₃×C₄×C₅	—	2	4	no	—
62	C₂×C₃×C₄×C₅	—	2	4	no	—
63	C₂×C₃×C₄×C₅	—	2	8	no	—
64	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
65	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
66	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
67	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
68	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	#41	1	2	yes	—
70	C₃×C₅×C₈	—	2	4	no	—
71	C₃×C₅×C₈	—	4	2	no	—
72	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
73	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
74	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
75	C₃×C₄⋊Q₈	—	2	1	no	—
76	C₃×C₄⋊Q₈	—	2	1	no	—
77	C₃×C₄⋊Q₈	—	2	2	no	—
78	C₂×C₃×C₄⋊C₄	C₄×C₅	1	4	yes	—
79	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
80	C₃×C₄⋊C₈	—	2	2	no	—
81	C₃×#101	—	2	8	no	—
82	C₃×#97	—	2	1	no	—
83	C₃×C₄×C₈	—	2	1	no	—
84	C₂×C₅×Q₈	—	2	2	no	—
85	C₂×C₅×Q₈	—	2	2	no	—
86	C₂×C₅×Q₈	—	2	4	no	—
87	C₂×C₅×Q₈	—	2	4	no	—
88	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
89	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
90	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
91	C₅×M₁₆	—	2	2	no	—
92	C₅×M₁₆	—	2	4	no	—
93	C₅×M₁₆	C₃×D₄	1	4	yes	—
94	C₂×C₅×C₈	—	2	2	no	—
95	C₂×C₅×C₈	—	2	2	no	—
96	C₅×C₄⋊C₄	—	2	4	no	—
97	C₅×C₄⋊C₄	—	2	4	no	—
98	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
99	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
100	C₄²×C₅	C₃×D₄	1	2	yes	—
101	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
102	#423	C₂×C₃×C₅	1	1	yes	characteristic
103	C₂×#101	C₂×C₃×C₅	1	4	yes	—
104	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic
105	C₂²×C₃×C₅	—	2	2	no	—
106	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
108	C₃×C₄×C₅	—	2	2	no	—
109	C₃×C₄×C₅	—	4	4	no	—
110	C₃×C₄×C₅	#101	1	4	yes	complemented
111	C₃×C₄×C₅	#121	1	2	yes	—
112	C₃×C₄×C₅	#124	1	1	yes	characteristic
113	C₃×C₄×C₅	#127	1	1	yes	characteristic
114	C₂×C₃×Q₈	—	2	4	no	—
115	C₂×C₃×Q₈	—	2	2	no	—
116	C₂×C₃×Q₈	—	2	2	no	—
117	C₂×C₃×Q₈	—	2	4	no	—
118	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
119	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
120	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
121	C₃×M₁₆	—	2	2	no	—
122	C₃×M₁₆	—	2	4	no	—
123	C₃×M₁₆	C₅×D₄	1	4	yes	—
124	C₂×C₃×C₈	—	2	2	no	—
125	C₂×C₃×C₈	—	2	2	no	—
126	C₃×C₄⋊C₄	—	2	4	no	—
127	C₃×C₄⋊C₄	—	2	4	no	—
128	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
129	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
130	C₃×C₄²	C₅×D₄	1	2	yes	—
131	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
132	C₅×Q₈	—	4	4	no	—
133	C₅×Q₈	—	4	2	no	—
134	C₅×Q₈	—	4	2	no	—
135	C₂×C₄×C₅	—	2	4	no	—
136	C₂×C₄×C₅	—	2	4	no	—
137	C₂×C₄×C₅	—	2	8	no	—
138	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
139	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
140	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
141	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
142	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
143	C₂×C₄×C₅	C₃×#41	1	2	yes	—
144	C₅×C₈	—	2	4	no	—
145	C₅×C₈	—	4	2	no	—
146	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
147	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
148	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
149	C₄⋊Q₈	—	2	1	no	—
150	C₄⋊Q₈	—	2	1	no	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₂×C₄⋊C₄	C₃×C₄×C₅	1	4	yes	—
153	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
154	C₄⋊C₈	—	2	2	no	—
155	#101	—	2	8	no	—
156	#97	—	2	1	no	—
157	C₄×C₈	—	2	1	no	—
158	C₂×C₃×C₅	—	2	2	no	—
159	C₂×C₃×C₅	#390	1	1	yes	characteristic
160	C₂×C₃×C₅	C₂×#101	1	2	yes	—
161	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
162	C₃×Q₈	—	4	4	no	—
163	C₃×Q₈	—	4	2	no	—
164	C₃×Q₈	—	4	2	no	—
165	C₂×C₃×C₄	—	2	4	no	—
166	C₂×C₃×C₄	—	2	4	no	—
167	C₂×C₃×C₄	—	2	8	no	—
168	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
169	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
170	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
171	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
172	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
173	C₂×C₃×C₄	C₅×#41	1	2	yes	—
174	C₃×C₈	—	2	4	no	—
175	C₃×C₈	—	4	2	no	—
176	C₂²×C₅	—	2	2	no	—
177	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
179	C₄×C₅	—	2	2	no	—
180	C₄×C₅	—	4	4	no	—
181	C₄×C₅	C₃×#101	1	4	yes	complemented
182	C₄×C₅	C₃×#121	1	2	yes	—
183	C₄×C₅	C₃×#124	1	1	yes	characteristic
184	C₄×C₅	C₃×#127	1	1	yes	characteristic
185	C₂×Q₈	—	2	4	no	—
186	C₂×Q₈	—	2	2	no	—
187	C₂×Q₈	—	2	2	no	—
188	C₂×Q₈	—	2	4	no	—
189	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
190	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
191	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
192	M₁₆	—	2	2	no	—
193	M₁₆	—	2	4	no	—
194	M₁₆	C₃×C₅×D₄	1	4	yes	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₄⋊C₄	—	2	4	no	—
198	C₄⋊C₄	—	2	4	no	—
199	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
200	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
201	C₄²	C₃×C₅×D₄	1	2	yes	—
202	C₃×C₅	#1966	1	1	yes	characteristic, direct product factor, Hall
203	C₂²×C₃	—	2	2	no	—
204	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
206	C₃×C₄	—	2	2	no	—
207	C₃×C₄	—	4	4	no	—
208	C₃×C₄	C₅×#101	1	4	yes	complemented
209	C₃×C₄	C₅×#121	1	2	yes	—
210	C₃×C₄	C₅×#124	1	1	yes	characteristic
211	C₃×C₄	C₅×#127	1	1	yes	characteristic
212	C₂×C₅	—	2	2	no	—
213	C₂×C₅	C₃×#390	1	1	yes	characteristic
214	C₂×C₅	C₂×C₃×#101	1	2	yes	—
215	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
216	Q₈	—	4	4	no	—
217	Q₈	—	4	2	no	—
218	Q₈	—	4	2	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	2	8	no	—
222	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
223	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
224	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
225	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
226	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
227	C₂×C₄	C₃×C₅×#41	1	2	yes	—
228	C₈	—	2	4	no	—
229	C₈	—	4	2	no	—
230	C₂×C₃	—	2	2	no	—
231	C₂×C₃	C₅×#390	1	1	yes	characteristic
232	C₂×C₃	C₂×C₅×#101	1	2	yes	—
233	C₅	C₃×#1966	1	1	yes	characteristic, direct product factor, Sylow
234	C₂²	—	2	2	no	—
235	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²	C₃×C₄×C₅×D₄	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	4	4	no	—
239	C₄	C₃×C₅×#101	1	4	yes	complemented
240	C₄	C₃×C₅×#121	1	2	yes	—
241	C₄	C₃×C₅×#124	1	1	yes	characteristic
242	C₄	C₃×C₅×#127	1	1	yes	characteristic
243	C₃	C₅×#1966	1	1	yes	characteristic, direct product factor, Sylow
244	C₂	—	2	2	no	—
245	C₂	C₃×C₅×#390	1	1	yes	characteristic
246	C₂	C₂×C₃×C₅×#101	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂³×C₃×C₅	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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×#1966	C₃	direct (N × H)
18. C₃×#1966	C₅	direct (N × H)
56. #1966	C₃×C₅	direct (N × H)
110. C₃×C₄×C₅	#101	semidirect
181. C₄×C₅	C₃×#101	semidirect
202. C₃×C₅	#1966	direct (N × H)
208. C₃×C₄	C₅×#101	semidirect
233. C₅	C₃×#1966	direct (N × H)
239. C₄	C₃×C₅×#101	semidirect
243. C₃	C₅×#1966	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×C₄⋊Q₈	2
C₃×C₅×#423	2
C₂×C₃×C₅×#101	2
C₃×C₄×C₅×M₁₆	2
C₅×#1966	3
C₃×#1966	5

Subgroups — C3×C5×#1966 #14275000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1966 #14275000