Subgroups — C₅×#70444 #14298739

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 216 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⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#4932	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₅×#4550	C₂	1	4	yes	maximal
5	C₅×#1832	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
9	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
10	C₃×C₅×C₄⋊C₈	—	2	2	no	—
11	C₅×C₃⋊#95	C₄	1	2	yes	—
12	C₅×C₃⋊#95	C₄	1	2	yes	—
13	C₅×C₄⋊(C₃⋊C₈)	—	2	2	no	—
14	#70444	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×C₄⋊C₈	—	3	1	no	—
16	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic
17	C₅×#376	—	3	1	no	—
18	C₅×#336	—	3	4	no	—
19	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
23	C₂×C₃×C₅×C₈	—	2	2	no	—
24	C₂×C₃×C₅×C₈	—	2	4	no	—
25	C₃×C₄²×C₅	D₄	1	2	yes	—
26	C₃×C₄²×C₅	Q₈	1	2	yes	—
27	C₄×C₅×Dic₃	—	2	2	no	—
28	C₄×C₅×Dic₃	—	2	2	no	—
29	C₂×C₅×C₃⋊C₈	—	2	2	no	—
30	C₂×C₅×C₃⋊C₈	—	2	4	no	—
31	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
32	#4932	C₂×C₅	1	1	yes	characteristic
33	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic
34	#4550	C₂×C₅	1	4	yes	—
35	C₂²×C₅×C₈	—	3	2	no	—
36	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
37	C₂×C₄²×C₅	—	3	2	no	—
38	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
39	C₅×C₄⋊C₈	—	2	2	no	—
40	C₅×C₄⋊C₈	—	6	2	no	—
41	C₅×#95	—	3	2	no	—
42	C₅×#95	—	3	2	no	—
43	#1832	—	3	1	no	Sylow
44	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×C₅	—	2	2	no	—
46	C₂×C₃×C₄×C₅	—	2	2	no	—
47	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
48	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
49	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	#41	1	2	yes	—
52	C₂×C₃×C₄×C₅	#41	1	2	yes	—
53	C₂×C₅×Dic₃	—	2	4	no	—
54	C₂×C₅×Dic₃	—	2	4	no	—
55	C₂×C₅×Dic₃	—	2	4	no	—
56	C₃×C₅×C₈	—	4	2	no	—
57	C₅×C₃⋊C₈	—	4	2	no	—
58	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
59	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
60	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
61	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
62	C₃×C₄⋊C₈	—	2	2	no	—
63	C₃⋊#95	C₄×C₅	1	2	yes	—
64	C₃⋊#95	C₄×C₅	1	2	yes	—
65	C₄⋊(C₃⋊C₈)	—	2	2	no	—
66	C₂²×C₄×C₅	—	3	4	no	—
67	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
68	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
69	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
70	C₂×C₅×C₈	—	2	4	no	—
71	C₂×C₅×C₈	—	2	2	no	—
72	C₂×C₅×C₈	—	6	4	no	—
73	C₂×C₅×C₈	—	6	2	no	—
74	C₄²×C₅	—	6	2	no	—
75	C₄²×C₅	—	6	2	no	—
76	C₄²×C₅	Dic₆	1	2	yes	—
77	C₄²×C₅	#67	1	2	yes	—
78	C₂×C₄⋊C₈	—	3	1	no	—
79	C₂×C₄⋊C₈	C₅×D₃	1	1	yes	characteristic
80	#376	—	3	1	no	—
81	#336	—	3	4	no	—
82	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₃×C₅	#117	1	2	yes	—
84	C₂²×C₃×C₅	#131	1	2	yes	—
85	C₂²×C₃×C₅	#131	1	2	yes	—
86	C₃×C₄×C₅	—	2	2	no	—
87	C₃×C₄×C₅	—	2	2	no	—
88	C₃×C₄×C₅	#124	1	1	yes	characteristic
89	C₃×C₄×C₅	#124	1	1	yes	characteristic
90	C₃×C₄×C₅	#125	1	2	yes	—
91	C₅×Dic₃	—	4	4	no	—
92	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
93	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
94	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
95	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
96	C₂×C₃×C₈	—	2	2	no	—
97	C₂×C₃×C₈	—	2	4	no	—
98	C₃×C₄²	C₅×D₄	1	2	yes	—
99	C₃×C₄²	C₅×Q₈	1	2	yes	—
100	C₄×Dic₃	—	2	2	no	—
101	C₄×Dic₃	—	2	2	no	—
102	C₂×C₃⋊C₈	—	2	2	no	—
103	C₂×C₃⋊C₈	—	2	4	no	—
104	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
105	C₂×C₄×C₅	—	2	2	no	—
106	C₂×C₄×C₅	—	2	2	no	—
107	C₂×C₄×C₅	—	6	4	no	—
108	C₂×C₄×C₅	—	6	4	no	—
109	C₂×C₄×C₅	—	6	4	no	—
110	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
111	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
112	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
113	C₂×C₄×C₅	#237	1	2	yes	—
114	C₂×C₄×C₅	#239	1	2	yes	—
115	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
116	C₅×C₈	—	4	2	no	—
117	C₅×C₈	—	12	2	no	—
118	C₂²×C₈	—	3	2	no	—
119	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
120	C₂×C₄²	—	3	2	no	—
121	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
122	C₄⋊C₈	—	2	2	no	—
123	C₄⋊C₈	—	6	2	no	—
124	#95	—	3	2	no	—
125	#95	—	3	2	no	—
126	C₂×C₃×C₅	#382	1	1	yes	characteristic
127	C₂×C₃×C₅	#424	1	1	yes	characteristic
128	C₂×C₃×C₅	#424	1	1	yes	characteristic
129	C₂×C₃×C₅	#433	1	4	yes	—
130	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
131	C₂×C₃×C₄	—	2	2	no	—
132	C₂×C₃×C₄	—	2	2	no	—
133	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
134	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
135	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
137	C₂×C₃×C₄	C₅×#41	1	2	yes	—
138	C₂×C₃×C₄	C₅×#41	1	2	yes	—
139	C₂×Dic₃	—	2	4	no	—
140	C₂×Dic₃	—	2	4	no	—
141	C₂×Dic₃	—	2	4	no	—
142	C₃×C₈	—	4	2	no	—
143	C₃⋊C₈	—	4	2	no	—
144	C₂²×C₅	#892	1	2	yes	—
145	C₂²×C₅	#901	1	2	yes	—
146	C₂²×C₅	#907	1	2	yes	—
147	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
148	C₄×C₅	—	2	2	no	—
149	C₄×C₅	—	2	2	no	—
150	C₄×C₅	—	12	4	no	—
151	C₄×C₅	#890	1	2	yes	—
152	C₄×C₅	#936	1	1	yes	characteristic
153	C₄×C₅	#947	1	1	yes	characteristic
154	C₂²×C₄	—	3	4	no	—
155	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
156	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
157	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	6	4	no	—
161	C₂×C₈	—	6	2	no	—
162	C₄²	—	6	2	no	—
163	C₄²	—	6	2	no	—
164	C₄²	C₅×Dic₆	1	2	yes	—
165	C₄²	C₅×#67	1	2	yes	—
166	C₃×C₅	#1832	1	1	yes	characteristic, complemented, Hall
167	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₃	C₅×#117	1	2	yes	—
169	C₂²×C₃	C₅×#131	1	2	yes	—
170	C₂²×C₃	C₅×#131	1	2	yes	—
171	C₃×C₄	—	2	2	no	—
172	C₃×C₄	—	2	2	no	—
173	C₃×C₄	C₅×#124	1	1	yes	characteristic
174	C₃×C₄	C₅×#124	1	1	yes	characteristic
175	C₃×C₄	C₅×#125	1	2	yes	—
176	Dic₃	—	4	4	no	—
177	C₂×C₅	#4840	1	4	yes	—
178	C₂×C₅	#4977	1	1	yes	characteristic
179	C₂×C₅	#5102	1	1	yes	characteristic
180	C₂×C₅	#5119	1	1	yes	characteristic
181	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	6	4	no	—
185	C₂×C₄	—	6	4	no	—
186	C₂×C₄	—	6	4	no	—
187	C₂×C₄	C₅×Dic₃⋊C₄	1	2	yes	—
188	C₂×C₄	C₅×Dic₃⋊C₄	1	2	yes	—
189	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
190	C₂×C₄	C₅×#237	1	2	yes	—
191	C₂×C₄	C₅×#239	1	2	yes	—
192	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
193	C₈	—	4	2	no	—
194	C₈	—	12	2	no	—
195	C₂×C₃	C₅×#382	1	1	yes	characteristic
196	C₂×C₃	C₅×#424	1	1	yes	characteristic
197	C₂×C₃	C₅×#424	1	1	yes	characteristic
198	C₂×C₃	C₅×#433	1	4	yes	—
199	C₅	#70444	1	1	yes	characteristic, direct product factor, Sylow
200	C₂²	C₅×#892	1	2	yes	—
201	C₂²	C₅×#901	1	2	yes	—
202	C₂²	C₅×#907	1	2	yes	—
203	C₂²	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
204	C₄	—	2	2	no	—
205	C₄	—	2	2	no	—
206	C₄	—	12	4	no	—
207	C₄	C₅×#890	1	2	yes	—
208	C₄	C₅×#936	1	1	yes	characteristic
209	C₄	C₅×#947	1	1	yes	characteristic
210	C₃	C₅×#1832	1	1	yes	characteristic, complemented, Sylow
211	C₂	C₅×#4840	1	4	yes	—
212	C₂	C₅×#4977	1	1	yes	characteristic
213	C₂	C₅×#5102	1	1	yes	characteristic
214	C₂	C₅×#5119	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₅×#1832
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
14. #70444	C₅	direct (N × H)
166. C₃×C₅	#1832	semidirect
199. C₅	#70444	direct (N × H)
210. C₃	C₅×#1832	semidirect

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⋊C₈	2
C₅×#4932	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4550	2
C₅×#1832	3
#70444	5

Subgroups — C5×#70444 #14298739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70444 #14298739