Subgroups — C₃×C₅×#2074 #14275108

Order 1920.

444 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal
2	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#340	C₂	1	2	yes	maximal
5	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic
6	C₅×#2074	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₃×C₅×#103	—	2	4	no	—
13	C₃×C₅×#95	—	2	2	no	—
14	C₃×C₅×#95	—	2	2	no	—
15	C₃×#2074	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×#103	C₂×C₃	1	2	yes	—
17	C₅×#391	C₂×C₃	1	1	yes	characteristic
18	C₅×#382	C₂×C₃	1	1	yes	characteristic
19	C₅×#340	C₂×C₃	1	2	yes	—
20	C₅×#336	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃×C₅×Q₈	—	2	1	no	—
22	C₂×C₃×C₅×Q₈	—	2	2	no	—
23	C₂×C₃×C₅×Q₈	—	2	2	no	—
24	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
25	C₂²×C₃×C₄×C₅	—	2	1	no	—
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	—	2	1	no	—
28	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₂×C₃×C₅×C₈	—	2	2	no	—
31	C₂×C₃×C₅×C₈	—	2	2	no	—
32	C₂×C₃×C₅×C₈	—	2	2	no	—
33	C₃×C₅×C₄⋊C₄	—	2	2	no	—
34	C₃×C₅×C₄⋊C₄	—	2	2	no	—
35	C₃×C₅×C₄⋊C₄	—	2	2	no	—
36	C₃×C₄²×C₅	—	2	2	no	—
37	C₂×C₃×#103	C₂×C₅	1	2	yes	—
38	C₃×#391	C₂×C₅	1	1	yes	characteristic
39	C₃×#382	C₂×C₅	1	1	yes	characteristic
40	C₃×#340	C₂×C₅	1	2	yes	—
41	C₃×#336	C₂×C₅	1	1	yes	characteristic
42	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
44	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
45	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
46	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
47	C₅×#103	—	2	4	no	—
48	C₅×#95	—	2	2	no	—
49	C₅×#95	—	2	2	no	—
50	#2074	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
51	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
52	C₃×C₅×Q₈	—	2	4	no	—
53	C₃×C₅×Q₈	—	4	2	no	—
54	C₂×C₃×C₄×C₅	—	2	2	no	—
55	C₂×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₃×C₄×C₅	—	2	2	no	—
57	C₂×C₃×C₄×C₅	—	2	2	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	—	4	1	no	—
62	C₂×C₃×C₄×C₅	—	4	2	no	—
63	C₂×C₃×C₄×C₅	—	4	2	no	—
64	C₂×C₃×C₄×C₅	—	4	2	no	—
65	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
66	C₂×C₃×C₄×C₅	#41	1	2	yes	—
67	C₂×C₃×C₄×C₅	#41	1	2	yes	—
68	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
69	C₃×C₅×C₈	—	4	2	no	—
70	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
71	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
72	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
73	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
74	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
75	C₃×#103	—	2	4	no	—
76	C₃×#95	—	2	2	no	—
77	C₃×#95	—	2	2	no	—
78	C₂×C₅×Q₈	—	2	1	no	—
79	C₂×C₅×Q₈	—	2	2	no	—
80	C₂×C₅×Q₈	—	2	2	no	—
81	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
82	C₂²×C₄×C₅	—	2	1	no	—
83	C₂²×C₄×C₅	—	2	2	no	—
84	C₂²×C₄×C₅	—	2	1	no	—
85	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
86	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
87	C₂×C₅×C₈	—	2	2	no	—
88	C₂×C₅×C₈	—	2	2	no	—
89	C₂×C₅×C₈	—	2	2	no	—
90	C₅×C₄⋊C₄	—	2	2	no	—
91	C₅×C₄⋊C₄	—	2	2	no	—
92	C₅×C₄⋊C₄	—	2	2	no	—
93	C₄²×C₅	—	2	2	no	—
94	C₂×#103	C₂×C₃×C₅	1	2	yes	—
95	#391	C₂×C₃×C₅	1	1	yes	characteristic
96	#382	C₂×C₃×C₅	1	1	yes	characteristic
97	#340	C₂×C₃×C₅	1	2	yes	—
98	#336	C₂×C₃×C₅	1	1	yes	characteristic
99	C₂²×C₃×C₅	#121	1	1	yes	characteristic
100	C₂²×C₃×C₅	#123	1	1	yes	characteristic
101	C₂²×C₃×C₅	#124	1	1	yes	characteristic
102	C₂²×C₃×C₅	#135	1	2	yes	—
103	C₂²×C₃×C₅	#137	1	2	yes	—
104	C₃×C₄×C₅	—	4	2	no	—
105	C₃×C₄×C₅	—	4	2	no	—
106	C₃×C₄×C₅	—	8	2	no	—
107	C₃×C₄×C₅	—	8	1	no	—
108	C₃×C₄×C₅	#123	1	2	yes	—
109	C₃×C₄×C₅	#126	1	2	yes	—
110	C₂×C₃×Q₈	—	2	1	no	—
111	C₂×C₃×Q₈	—	2	2	no	—
112	C₂×C₃×Q₈	—	2	2	no	—
113	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
114	C₂²×C₃×C₄	—	2	1	no	—
115	C₂²×C₃×C₄	—	2	2	no	—
116	C₂²×C₃×C₄	—	2	1	no	—
117	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
118	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
119	C₂×C₃×C₈	—	2	2	no	—
120	C₂×C₃×C₈	—	2	2	no	—
121	C₂×C₃×C₈	—	2	2	no	—
122	C₃×C₄⋊C₄	—	2	2	no	—
123	C₃×C₄⋊C₄	—	2	2	no	—
124	C₃×C₄⋊C₄	—	2	2	no	—
125	C₃×C₄²	—	2	2	no	—
126	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
127	C₅×Q₈	—	2	4	no	—
128	C₅×Q₈	—	4	2	no	—
129	C₂×C₄×C₅	—	2	2	no	—
130	C₂×C₄×C₅	—	2	2	no	—
131	C₂×C₄×C₅	—	2	2	no	—
132	C₂×C₄×C₅	—	2	2	no	—
133	C₂×C₄×C₅	—	4	1	no	—
134	C₂×C₄×C₅	—	4	1	no	—
135	C₂×C₄×C₅	—	4	2	no	—
136	C₂×C₄×C₅	—	4	1	no	—
137	C₂×C₄×C₅	—	4	2	no	—
138	C₂×C₄×C₅	—	4	2	no	—
139	C₂×C₄×C₅	—	4	2	no	—
140	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
141	C₂×C₄×C₅	C₃×#41	1	2	yes	—
142	C₂×C₄×C₅	C₃×#41	1	2	yes	—
143	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
144	C₅×C₈	—	4	2	no	—
145	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
146	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
147	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
148	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
149	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
150	#103	—	2	4	no	—
151	#95	—	2	2	no	—
152	#95	—	2	2	no	—
153	C₂×C₃×C₅	#397	1	1	yes	characteristic
154	C₂×C₃×C₅	#464	1	2	yes	—
155	C₂×C₃×C₅	#485	1	2	yes	—
156	C₂×C₃×C₅	#488	1	1	yes	characteristic
157	C₂×C₃×C₅	#491	1	1	yes	characteristic
158	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
159	C₃×Q₈	—	2	4	no	—
160	C₃×Q₈	—	4	2	no	—
161	C₂×C₃×C₄	—	2	2	no	—
162	C₂×C₃×C₄	—	2	2	no	—
163	C₂×C₃×C₄	—	2	2	no	—
164	C₂×C₃×C₄	—	2	2	no	—
165	C₂×C₃×C₄	—	4	1	no	—
166	C₂×C₃×C₄	—	4	1	no	—
167	C₂×C₃×C₄	—	4	2	no	—
168	C₂×C₃×C₄	—	4	1	no	—
169	C₂×C₃×C₄	—	4	2	no	—
170	C₂×C₃×C₄	—	4	2	no	—
171	C₂×C₃×C₄	—	4	2	no	—
172	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
173	C₂×C₃×C₄	C₅×#41	1	2	yes	—
174	C₂×C₃×C₄	C₅×#41	1	2	yes	—
175	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
176	C₃×C₈	—	4	2	no	—
177	C₂²×C₅	C₃×#121	1	1	yes	characteristic
178	C₂²×C₅	C₃×#123	1	1	yes	characteristic
179	C₂²×C₅	C₃×#124	1	1	yes	characteristic
180	C₂²×C₅	C₃×#135	1	2	yes	—
181	C₂²×C₅	C₃×#137	1	2	yes	—
182	C₄×C₅	—	4	2	no	—
183	C₄×C₅	—	4	2	no	—
184	C₄×C₅	—	8	2	no	—
185	C₄×C₅	—	8	1	no	—
186	C₄×C₅	C₃×#123	1	2	yes	—
187	C₄×C₅	C₃×#126	1	2	yes	—
188	C₂×Q₈	—	2	1	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	2	2	no	—
191	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
192	C₂²×C₄	—	2	1	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	2	1	no	—
195	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
196	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₄⋊C₄	—	2	2	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄²	—	2	2	no	—
204	C₃×C₅	#2074	1	1	yes	characteristic, direct product factor, Hall
205	C₂²×C₃	C₅×#121	1	1	yes	characteristic
206	C₂²×C₃	C₅×#123	1	1	yes	characteristic
207	C₂²×C₃	C₅×#124	1	1	yes	characteristic
208	C₂²×C₃	C₅×#135	1	2	yes	—
209	C₂²×C₃	C₅×#137	1	2	yes	—
210	C₃×C₄	—	4	2	no	—
211	C₃×C₄	—	4	2	no	—
212	C₃×C₄	—	8	2	no	—
213	C₃×C₄	—	8	1	no	—
214	C₃×C₄	C₅×#123	1	2	yes	—
215	C₃×C₄	C₅×#126	1	2	yes	—
216	C₂×C₅	C₃×#397	1	1	yes	characteristic
217	C₂×C₅	C₃×#464	1	2	yes	—
218	C₂×C₅	C₃×#485	1	2	yes	—
219	C₂×C₅	C₃×#488	1	1	yes	characteristic
220	C₂×C₅	C₃×#491	1	1	yes	characteristic
221	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
222	Q₈	—	2	4	no	—
223	Q₈	—	4	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
236	C₂×C₄	C₃×C₅×#41	1	2	yes	—
237	C₂×C₄	C₃×C₅×#41	1	2	yes	—
238	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
239	C₈	—	4	2	no	—
240	C₂×C₃	C₅×#397	1	1	yes	characteristic
241	C₂×C₃	C₅×#464	1	2	yes	—
242	C₂×C₃	C₅×#485	1	2	yes	—
243	C₂×C₃	C₅×#488	1	1	yes	characteristic
244	C₂×C₃	C₅×#491	1	1	yes	characteristic
245	C₅	C₃×#2074	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²	C₃×C₅×#121	1	1	yes	characteristic
247	C₂²	C₃×C₅×#123	1	1	yes	characteristic
248	C₂²	C₃×C₅×#124	1	1	yes	characteristic
249	C₂²	C₃×C₅×#135	1	2	yes	—
250	C₂²	C₃×C₅×#137	1	2	yes	—
251	C₄	—	4	2	no	—
252	C₄	—	4	2	no	—
253	C₄	—	8	2	no	—
254	C₄	—	8	1	no	—
255	C₄	C₃×C₅×#123	1	2	yes	—
256	C₄	C₃×C₅×#126	1	2	yes	—
257	C₃	C₅×#2074	1	1	yes	characteristic, direct product factor, Sylow
258	C₂	C₃×C₅×#397	1	1	yes	characteristic
259	C₂	C₃×C₅×#464	1	2	yes	—
260	C₂	C₃×C₅×#485	1	2	yes	—
261	C₂	C₃×C₅×#488	1	1	yes	characteristic
262	C₂	C₃×C₅×#491	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂²×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
6. C₅×#2074	C₃	direct (N × H)
15. C₃×#2074	C₅	direct (N × H)
50. #2074	C₃×C₅	direct (N × H)
204. C₃×C₅	#2074	direct (N × H)
245. C₅	C₃×#2074	direct (N × H)
257. C₃	C₅×#2074	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×#103	2
C₃×C₅×#391	2
C₃×C₅×#382	2
C₃×C₅×#340	2
C₃×C₅×#336	2
C₅×#2074	3
C₃×#2074	5

Subgroups — C3×C5×#2074 #14275108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2074 #14275108