Subgroups — C₅×#67720 #14278875

Order 1920.

272 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#819	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#812	C₂	1	1	yes	maximal, characteristic
4	C₅×#1383	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
7	C₂×C₅×#208	—	2	1	no	—
8	C₃×C₅×#106	—	2	1	no	—
9	C₃×C₅×#106	C₄	1	2	yes	—
10	C₅×#819	—	2	1	no	—
11	C₅×#819	C₄	1	2	yes	complemented
12	C₅×#812	—	2	1	no	—
13	C₅×#812	—	2	1	no	—
14	C₂×C₅×C₃⋊C₁₆	C₄	1	2	yes	complemented
15	#67720	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×M₃₂	—	3	1	no	—
17	C₂×C₅×#108	—	3	1	no	—
18	C₂×C₅×#106	D₃	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₅	—	4	1	no	—
20	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
21	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
25	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
26	C₂×C₃×C₅×C₈	Q₈	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₄	—	2	2	no	—
28	C₃×C₅×C₄⋊C₄	—	4	1	no	—
29	C₅×#208	—	2	2	no	—
30	C₅×#208	—	4	1	no	—
31	C₂×C₅×C₃⋊C₈	—	4	1	no	—
32	C₅×C₃⋊C₁₆	—	2	2	no	—
33	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic
34	C₂×#819	C₂×C₅	1	1	yes	characteristic
35	C₂×#812	C₂×C₅	1	1	yes	characteristic
36	C₂×C₅×M₁₆	—	6	1	no	—
37	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₄	—	2	1	no	—
39	C₅×M₃₂	—	6	1	no	—
40	C₅×M₃₂	—	6	1	no	—
41	C₂×C₅×C₁₆	—	3	2	no	—
42	C₅×#108	—	3	2	no	—
43	C₅×#108	—	6	1	no	—
44	C₅×#106	—	2	1	no	—
45	C₅×#106	Dic₃	1	2	yes	—
46	#1383	—	3	1	no	Sylow
47	C₂³×C₃×C₅	SD₁₆	1	1	yes	characteristic
48	C₂×C₃×C₄×C₅	—	4	2	no	—
49	C₂×C₃×C₄×C₅	—	8	2	no	—
50	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
54	C₂×C₃×C₄×C₅	SD₁₆	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	Q₁₆	1	1	yes	characteristic
56	C₃×C₅×C₈	C₄²	1	1	yes	characteristic
57	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
58	C₃×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
59	C₃×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
60	C₅×C₃⋊C₈	—	4	2	no	—
61	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
62	C₂×C₃×C₄⋊C₄	—	2	1	no	—
63	C₂×#208	—	2	1	no	—
64	C₃×#106	—	2	1	no	—
65	C₃×#106	C₄×C₅	1	2	yes	—
66	#819	—	2	1	no	—
67	#819	C₄×C₅	1	2	yes	complemented
68	#812	—	2	1	no	—
69	#812	—	2	1	no	—
70	C₂×C₃⋊C₁₆	C₄×C₅	1	2	yes	complemented
71	C₂²×C₄×C₅	—	4	1	no	—
72	C₂²×C₄×C₅	#67	1	1	yes	characteristic
73	C₅×M₁₆	—	6	2	no	—
74	C₅×M₁₆	—	12	1	no	—
75	C₂×C₅×C₈	—	12	1	no	—
76	C₂×C₅×C₈	Dic₆	1	1	yes	characteristic
77	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
78	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
79	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
80	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
81	C₂×C₅×C₈	#67	1	1	yes	characteristic
82	C₅×C₄⋊C₄	—	2	2	no	—
83	C₅×C₄⋊C₄	—	4	1	no	—
84	C₅×C₁₆	—	6	2	no	—
85	C₂×M₃₂	—	3	1	no	—
86	C₂×#108	—	3	1	no	—
87	C₂×#106	C₅×D₃	1	1	yes	characteristic
88	C₂²×C₃×C₅	—	2	2	no	—
89	C₂²×C₃×C₅	#102	1	1	yes	characteristic
90	C₂²×C₃×C₅	#103	1	1	yes	characteristic
91	C₂²×C₃×C₅	#106	1	1	yes	characteristic
92	C₃×C₄×C₅	—	8	2	no	—
93	C₃×C₄×C₅	#95	1	1	yes	characteristic
94	C₃×C₄×C₅	#102	1	1	yes	characteristic
95	C₃×C₄×C₅	#103	1	1	yes	characteristic
96	C₃×C₄×C₅	#107	1	1	yes	characteristic
97	C₂²×C₃×C₄	—	4	1	no	—
98	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
99	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
100	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
101	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
102	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
103	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
104	C₂×C₃×C₈	C₅×Q₈	1	1	yes	characteristic
105	C₃×C₄⋊C₄	—	2	2	no	—
106	C₃×C₄⋊C₄	—	4	1	no	—
107	#208	—	2	2	no	—
108	#208	—	4	1	no	—
109	C₂×C₃⋊C₈	—	4	1	no	—
110	C₃⋊C₁₆	—	2	2	no	—
111	C₂³×C₅	#214	1	1	yes	characteristic
112	C₂×C₄×C₅	—	4	2	no	—
113	C₂×C₄×C₅	—	8	2	no	—
114	C₂×C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
116	C₂×C₄×C₅	#213	1	1	yes	characteristic
117	C₂×C₄×C₅	#215	1	1	yes	characteristic
118	C₂×C₄×C₅	#216	1	1	yes	characteristic
119	C₂×C₄×C₅	#217	1	1	yes	characteristic
120	C₅×C₈	—	12	2	no	—
121	C₅×C₈	C₄×Dic₃	1	1	yes	characteristic
122	C₅×C₈	Dic₃⋊C₄	1	1	yes	characteristic
123	C₅×C₈	C₄⋊Dic₃	1	1	yes	characteristic
124	C₅×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
125	C₂×M₁₆	—	6	1	no	—
126	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
127	C₂×C₄⋊C₄	—	2	1	no	—
128	M₃₂	—	6	1	no	—
129	M₃₂	—	6	1	no	—
130	C₂×C₁₆	—	3	2	no	—
131	#108	—	3	2	no	—
132	#108	—	6	1	no	—
133	#106	—	2	1	no	—
134	#106	C₅×Dic₃	1	2	yes	—
135	C₂×C₃×C₅	—	2	1	no	—
136	C₂×C₃×C₅	—	2	1	no	—
137	C₂×C₃×C₅	#340	1	1	yes	characteristic
138	C₂×C₃×C₅	#365	1	2	yes	—
139	C₂³×C₃	C₅×SD₁₆	1	1	yes	characteristic
140	C₂×C₃×C₄	—	4	2	no	—
141	C₂×C₃×C₄	—	8	2	no	—
142	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₃×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₃×C₄	C₅×D₈	1	1	yes	characteristic
146	C₂×C₃×C₄	C₅×SD₁₆	1	1	yes	characteristic
147	C₂×C₃×C₄	C₅×Q₁₆	1	1	yes	characteristic
148	C₃×C₈	C₄²×C₅	1	1	yes	characteristic
149	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
150	C₃×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
151	C₃×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
152	C₃⋊C₈	—	4	2	no	—
153	C₂²×C₅	—	2	2	no	—
154	C₂²×C₅	#808	1	1	yes	characteristic
155	C₂²×C₅	#810	1	1	yes	characteristic
156	C₂²×C₅	#832	1	1	yes	characteristic
157	C₄×C₅	—	8	2	no	—
158	C₄×C₅	#807	1	1	yes	characteristic
159	C₄×C₅	#809	1	1	yes	characteristic
160	C₄×C₅	C₃⋊#95	1	1	yes	characteristic
161	C₄×C₅	#835	1	1	yes	characteristic
162	C₂²×C₄	—	4	1	no	—
163	C₂²×C₄	C₅×#67	1	1	yes	characteristic
164	M₁₆	—	6	2	no	—
165	M₁₆	—	12	1	no	—
166	C₂×C₈	—	12	1	no	—
167	C₂×C₈	C₅×Dic₆	1	1	yes	characteristic
168	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
169	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
170	C₂×C₈	C₅×D₁₂	1	1	yes	characteristic
171	C₂×C₈	C₂×C₅×Dic₃	1	1	yes	characteristic
172	C₂×C₈	C₅×#67	1	1	yes	characteristic
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	4	1	no	—
175	C₁₆	—	6	2	no	—
176	C₃×C₅	#1383	1	1	yes	characteristic, complemented, Hall
177	C₂²×C₃	—	2	2	no	—
178	C₂²×C₃	C₅×#102	1	1	yes	characteristic
179	C₂²×C₃	C₅×#103	1	1	yes	characteristic
180	C₂²×C₃	C₅×#106	1	1	yes	characteristic
181	C₃×C₄	—	8	2	no	—
182	C₃×C₄	C₅×#95	1	1	yes	characteristic
183	C₃×C₄	C₅×#102	1	1	yes	characteristic
184	C₃×C₄	C₅×#103	1	1	yes	characteristic
185	C₃×C₄	C₅×#107	1	1	yes	characteristic
186	C₂×C₅	—	2	1	no	—
187	C₂×C₅	—	2	1	no	—
188	C₂×C₅	#4487	1	2	yes	—
189	C₂×C₅	#4529	1	1	yes	characteristic
190	C₂³	C₅×#214	1	1	yes	characteristic
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	8	2	no	—
193	C₂×C₄	C₅×Dic₃⋊C₄	1	1	yes	characteristic
194	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
195	C₂×C₄	C₅×#213	1	1	yes	characteristic
196	C₂×C₄	C₅×#215	1	1	yes	characteristic
197	C₂×C₄	C₅×#216	1	1	yes	characteristic
198	C₂×C₄	C₅×#217	1	1	yes	characteristic
199	C₈	—	12	2	no	—
200	C₈	C₄×C₅×Dic₃	1	1	yes	characteristic
201	C₈	C₅×Dic₃⋊C₄	1	1	yes	characteristic
202	C₈	C₅×C₄⋊Dic₃	1	1	yes	characteristic
203	C₈	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
204	C₂×C₃	—	2	1	no	—
205	C₂×C₃	—	2	1	no	—
206	C₂×C₃	C₅×#340	1	1	yes	characteristic
207	C₂×C₃	C₅×#365	1	2	yes	—
208	C₅	#67720	1	1	yes	characteristic, direct product factor, Sylow
209	C₂²	—	2	2	no	—
210	C₂²	C₅×#808	1	1	yes	characteristic
211	C₂²	C₅×#810	1	1	yes	characteristic
212	C₂²	C₅×#832	1	1	yes	characteristic
213	C₄	—	8	2	no	—
214	C₄	C₅×#807	1	1	yes	characteristic
215	C₄	C₅×#809	1	1	yes	characteristic
216	C₄	C₅×C₃⋊#95	1	1	yes	characteristic
217	C₄	C₅×#835	1	1	yes	characteristic
218	C₃	C₅×#1383	1	1	yes	characteristic, complemented, Sylow
219	C₂	—	2	1	no	—
220	C₂	—	2	1	no	—
221	C₂	C₅×#4487	1	2	yes	—
222	C₂	C₅×#4529	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#808
commutator	C₃×C₈	C₄²×C₅
Frattini	C₂²×C₈	C₂×C₅×D₃
Fitting	C₂×C₃×C₅×#106	C₂
socle	C₂²×C₃×C₅	#106
prime radical	C₂³×C₃×C₅	SD₁₆
cosocle	C₂²×C₃×C₈	C₂²×C₅
hypercenter	C₂×C₅×#106	D₃
hypocenter	C₃	C₅×#1383
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂×C₅×#106

Complements

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

N	H ≅ G/N	type
11. C₅×#819	C₄	semidirect
14. C₂×C₅×C₃⋊C₁₆	C₄	semidirect
15. #67720	C₅	direct (N × H)
67. #819	C₄×C₅	semidirect
70. C₂×C₃⋊C₁₆	C₄×C₅	semidirect
176. C₃×C₅	#1383	semidirect
208. C₅	#67720	direct (N × H)
218. C₃	C₅×#1383	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×#106	2
C₂×C₅×#819	2
C₂×C₅×#812	2
C₅×#1383	3
#67720	5

Subgroups — C5×#67720 #14278875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#67720 #14278875