Subgroups — C₃×C₅×#1951 #14274985

Order 1920.

392 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#428	C₂	1	2	yes	maximal
3	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#343	C₂	1	2	yes	maximal
6	C₅×#1951	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	1	yes	characteristic
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₃×C₅×#108	C₄	1	4	yes	complemented
13	C₃×C₅×#107	—	2	2	no	—
14	C₃×C₅×#106	—	2	1	no	—
15	C₃×C₅×#106	—	2	1	no	—
16	C₃×C₅×#106	—	2	2	no	—
17	C₃×C₅×#97	—	2	1	no	—
18	C₃×C₄×C₅×C₈	—	2	1	no	—
19	C₃×#1951	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic
21	C₅×#428	C₂×C₃	1	2	yes	—
22	C₂×C₅×#106	C₂×C₃	1	1	yes	characteristic
23	C₅×#405	C₂×C₃	1	1	yes	characteristic
24	C₅×#343	C₂×C₃	1	2	yes	—
25	C₂²×C₃×C₄×C₅	—	2	2	no	—
26	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₃×C₅×M₁₆	—	2	2	no	—
28	C₃×C₅×M₁₆	—	2	1	no	—
29	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	—
30	C₃×C₅×M₁₆	Q₈	1	2	yes	—
31	C₂×C₃×C₅×C₈	—	2	1	no	—
32	C₂×C₃×C₅×C₈	—	2	2	no	—
33	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
34	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
35	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
36	C₂×C₃×C₅×C₈	Q₈	1	2	yes	—
37	C₃×C₅×C₄⋊C₄	—	2	2	no	—
38	C₃×C₅×C₄⋊C₄	—	2	2	no	—
39	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
40	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
41	C₃×C₄²×C₅	—	2	1	no	—
42	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic
43	C₃×#428	C₂×C₅	1	2	yes	—
44	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic
45	C₃×#405	C₂×C₅	1	1	yes	characteristic
46	C₃×#343	C₂×C₅	1	2	yes	—
47	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
48	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
50	C₅×#117	C₂²×C₃	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
52	C₅×#108	C₃×C₄	1	4	yes	complemented
53	C₅×#107	—	2	2	no	—
54	C₅×#106	—	2	1	no	—
55	C₅×#106	—	2	1	no	—
56	C₅×#106	—	2	2	no	—
57	C₅×#97	—	2	1	no	—
58	C₄×C₅×C₈	—	2	1	no	—
59	#1951	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
60	C₂³×C₃×C₅	#41	1	1	yes	characteristic
61	C₂×C₃×C₄×C₅	—	2	2	no	—
62	C₂×C₃×C₄×C₅	—	4	2	no	—
63	C₂×C₃×C₄×C₅	—	8	2	no	—
64	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
66	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
67	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
68	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
70	C₃×C₅×C₈	—	2	4	no	—
71	C₃×C₅×C₈	—	2	2	no	—
72	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
73	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
74	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
75	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
77	C₃×#117	C₂²×C₅	1	1	yes	characteristic
78	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
79	C₃×#108	C₄×C₅	1	4	yes	complemented
80	C₃×#107	—	2	2	no	—
81	C₃×#106	—	2	1	no	—
82	C₃×#106	—	2	1	no	—
83	C₃×#106	—	2	2	no	—
84	C₃×#97	—	2	1	no	—
85	C₃×C₄×C₈	—	2	1	no	—
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
88	C₅×M₁₆	—	2	2	no	—
89	C₅×M₁₆	—	2	1	no	—
90	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	—
91	C₅×M₁₆	C₃×Q₈	1	2	yes	—
92	C₂×C₅×C₈	—	2	1	no	—
93	C₂×C₅×C₈	—	2	2	no	—
94	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
95	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
96	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
97	C₂×C₅×C₈	C₃×Q₈	1	2	yes	—
98	C₅×C₄⋊C₄	—	2	2	no	—
99	C₅×C₄⋊C₄	—	2	2	no	—
100	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
101	C₅×C₂²⋊C₄	—	2	1	no	—
102	C₄²×C₅	—	2	1	no	—
103	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic
104	#428	C₂×C₃×C₅	1	2	yes	—
105	C₂×#106	C₂×C₃×C₅	1	1	yes	characteristic
106	#405	C₂×C₃×C₅	1	1	yes	characteristic
107	#343	C₂×C₃×C₅	1	2	yes	—
108	C₂²×C₃×C₅	—	2	2	no	—
109	C₂²×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
110	C₂²×C₃×C₅	#121	1	1	yes	characteristic
111	C₂²×C₃×C₅	#125	1	1	yes	characteristic
112	C₃×C₄×C₅	—	4	2	no	—
113	C₃×C₄×C₅	—	8	2	no	—
114	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
116	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
117	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
118	C₂²×C₃×C₄	—	2	2	no	—
119	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
120	C₃×M₁₆	—	2	2	no	—
121	C₃×M₁₆	—	2	1	no	—
122	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	—
123	C₃×M₁₆	C₅×Q₈	1	2	yes	—
124	C₂×C₃×C₈	—	2	1	no	—
125	C₂×C₃×C₈	—	2	2	no	—
126	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
127	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
128	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
129	C₂×C₃×C₈	C₅×Q₈	1	2	yes	—
130	C₃×C₄⋊C₄	—	2	2	no	—
131	C₃×C₄⋊C₄	—	2	2	no	—
132	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
133	C₃×C₂²⋊C₄	—	2	1	no	—
134	C₃×C₄²	—	2	1	no	—
135	C₂³×C₅	C₃×#41	1	1	yes	characteristic
136	C₂×C₄×C₅	—	2	2	no	—
137	C₂×C₄×C₅	—	4	2	no	—
138	C₂×C₄×C₅	—	8	2	no	—
139	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
140	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
141	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
142	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
145	C₅×C₈	—	2	4	no	—
146	C₅×C₈	—	2	2	no	—
147	C₅×C₈	C₃×C₄⋊C₄	1	2	yes	—
148	C₅×C₈	C₃×C₄⋊C₄	1	2	yes	—
149	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
150	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
151	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
152	#117	C₂²×C₃×C₅	1	1	yes	characteristic
153	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
154	#108	C₃×C₄×C₅	1	4	yes	complemented
155	#107	—	2	2	no	—
156	#106	—	2	1	no	—
157	#106	—	2	1	no	—
158	#106	—	2	2	no	—
159	#97	—	2	1	no	—
160	C₄×C₈	—	2	1	no	—
161	C₂×C₃×C₅	—	2	1	no	—
162	C₂×C₃×C₅	—	2	1	no	—
163	C₂×C₃×C₅	#389	1	1	yes	characteristic
164	C₂×C₃×C₅	#471	1	2	yes	—
165	C₂³×C₃	C₅×#41	1	1	yes	characteristic
166	C₂×C₃×C₄	—	2	2	no	—
167	C₂×C₃×C₄	—	4	2	no	—
168	C₂×C₃×C₄	—	8	2	no	—
169	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
170	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
171	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
172	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
173	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
174	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
175	C₃×C₈	—	2	4	no	—
176	C₃×C₈	—	2	2	no	—
177	C₃×C₈	C₅×C₄⋊C₄	1	2	yes	—
178	C₃×C₈	C₅×C₄⋊C₄	1	2	yes	—
179	C₂²×C₅	—	2	2	no	—
180	C₂²×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
181	C₂²×C₅	C₃×#121	1	1	yes	characteristic
182	C₂²×C₅	C₃×#125	1	1	yes	characteristic
183	C₄×C₅	—	4	2	no	—
184	C₄×C₅	—	8	2	no	—
185	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
187	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
188	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
189	C₂²×C₄	—	2	2	no	—
190	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
191	M₁₆	—	2	2	no	—
192	M₁₆	—	2	1	no	—
193	M₁₆	C₂×C₃×C₄×C₅	1	4	yes	—
194	M₁₆	C₃×C₅×Q₈	1	2	yes	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
198	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
199	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
200	C₂×C₈	C₃×C₅×Q₈	1	2	yes	—
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
204	C₂²⋊C₄	—	2	1	no	—
205	C₄²	—	2	1	no	—
206	C₃×C₅	#1951	1	1	yes	characteristic, direct product factor, Hall
207	C₂²×C₃	—	2	2	no	—
208	C₂²×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
209	C₂²×C₃	C₅×#121	1	1	yes	characteristic
210	C₂²×C₃	C₅×#125	1	1	yes	characteristic
211	C₃×C₄	—	4	2	no	—
212	C₃×C₄	—	8	2	no	—
213	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
214	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
215	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
216	C₃×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
217	C₂×C₅	—	2	1	no	—
218	C₂×C₅	—	2	1	no	—
219	C₂×C₅	C₃×#389	1	1	yes	characteristic
220	C₂×C₅	C₃×#471	1	2	yes	—
221	C₂³	C₃×C₅×#41	1	1	yes	characteristic
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	8	2	no	—
225	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
226	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
227	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
228	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
229	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
230	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
231	C₈	—	2	4	no	—
232	C₈	—	2	2	no	—
233	C₈	C₃×C₅×C₄⋊C₄	1	2	yes	—
234	C₈	C₃×C₅×C₄⋊C₄	1	2	yes	—
235	C₂×C₃	—	2	1	no	—
236	C₂×C₃	—	2	1	no	—
237	C₂×C₃	C₅×#389	1	1	yes	characteristic
238	C₂×C₃	C₅×#471	1	2	yes	—
239	C₅	C₃×#1951	1	1	yes	characteristic, direct product factor, Sylow
240	C₂²	—	2	2	no	—
241	C₂²	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
242	C₂²	C₃×C₅×#121	1	1	yes	characteristic
243	C₂²	C₃×C₅×#125	1	1	yes	characteristic
244	C₄	—	4	2	no	—
245	C₄	—	8	2	no	—
246	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
247	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
248	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
249	C₄	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
250	C₃	C₅×#1951	1	1	yes	characteristic, direct product factor, Sylow
251	C₂	—	2	1	no	—
252	C₂	—	2	1	no	—
253	C₂	C₃×C₅×#389	1	1	yes	characteristic
254	C₂	C₃×C₅×#471	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#121
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂³×C₃×C₅	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#1951	C₃	direct (N × H)
12. C₃×C₅×#108	C₄	semidirect
19. C₃×#1951	C₅	direct (N × H)
52. C₅×#108	C₃×C₄	semidirect
59. #1951	C₃×C₅	direct (N × H)
79. C₃×#108	C₄×C₅	semidirect
154. #108	C₃×C₄×C₅	semidirect
206. C₃×C₅	#1951	direct (N × H)
239. C₅	C₃×#1951	direct (N × H)
250. C₃	C₅×#1951	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×#108	2
C₃×C₅×#428	2
C₂×C₃×C₅×#106	2
C₃×C₅×#405	2
C₃×C₅×#343	2
C₅×#1951	3
C₃×#1951	5

Subgroups — C3×C5×#1951 #14274985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1951 #14274985