Subgroups — C₄×#91087 #14294208

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄³×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×#91087	C₂	1	4	yes	maximal
3	C₂×C₄×C₃⋊#168	C₂	1	2	yes	maximal
4	C₄×#3935	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄²×C₅	C₄	1	4	yes	—
6	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
8	C₂²×C₃⋊#168	C₂²	1	4	yes	—
9	#91087	C₄	1	16	yes	direct product factor
10	C₄×C₃⋊#168	C₄	1	8	yes	complemented
11	C₄×#803	—	5	1	no	maximal, Hall
12	C₄³×C₅	D₃	1	1	yes	characteristic
13	C₂×#3935	—	3	4	no	—
14	C₂×C₄×#168	—	3	2	no	—
15	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
16	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
17	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
18	C₃×C₄²×C₅	—	2	8	no	—
19	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
20	C₃×C₄²×C₅	C₂×C₄	1	8	yes	—
21	C₂×C₃⋊#168	C₂×C₄	1	8	yes	—
22	C₂×C₃⋊#168	C₂×C₄	1	16	yes	—
23	C₃×C₄³	D₅	1	1	yes	characteristic
24	C₂×#803	—	5	4	no	—
25	C₂×C₄×C₃⋊C₈	—	5	2	no	—
26	C₂×C₄²×C₅	Dic₃	1	4	yes	—
27	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
28	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
29	C₂²×#168	—	3	4	no	—
30	#3935	—	3	16	no	—
31	C₄×#168	—	3	8	no	—
32	C₄×#97	—	15	1	no	Sylow
33	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×C₅	—	2	8	no	—
35	C₂×C₃×C₄×C₅	C₄²	1	8	yes	—
36	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
37	C₂×C₃×C₄×C₅	M₁₆	1	8	yes	—
38	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
39	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
40	C₃⋊#168	C₄²	1	16	yes	complemented
41	C₂×C₃×C₄²	Dic₅	1	4	yes	—
42	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
43	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
44	C₂²×C₃⋊C₈	—	5	4	no	—
45	#803	—	5	16	no	—
46	C₄×C₃⋊C₈	—	5	8	no	—
47	C₂²×C₄×C₅	C₂×Dic₃	1	4	yes	—
48	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
49	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
50	C₄²×C₅	—	2	8	no	—
51	C₄²×C₅	C₄×D₃	1	4	yes	—
52	C₄²×C₅	C₄×D₃	1	8	yes	—
53	C₂×#168	—	3	8	no	—
54	C₂×#168	—	3	16	no	—
55	C₂×#97	—	15	4	no	—
56	C₂×C₄×C₈	—	15	2	no	—
57	C₄³	D₁₅	1	1	yes	characteristic
58	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
59	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
60	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	—
61	C₃×C₄×C₅	—	2	8	no	—
62	C₃×C₄×C₅	#97	1	8	yes	complemented
63	C₃×C₄×C₅	C₂×C₄²	1	4	yes	—
64	C₂²×C₃×C₄	C₂×Dic₅	1	4	yes	—
65	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
66	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
67	C₃×C₄²	—	2	8	no	—
68	C₃×C₄²	C₄×D₅	1	4	yes	—
69	C₃×C₄²	C₄×D₅	1	8	yes	—
70	C₂×C₃⋊C₈	—	5	8	no	—
71	C₂×C₃⋊C₈	—	5	16	no	—
72	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
73	C₂×C₄×C₅	—	2	8	no	—
74	C₂×C₄×C₅	#208	1	8	yes	—
75	C₂×C₄×C₅	C₄×Dic₃	1	8	yes	—
76	C₂×C₄×C₅	C₄×Dic₃	1	4	yes	—
77	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
78	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
79	#168	—	3	16	no	—
80	C₂²×C₈	—	15	4	no	—
81	C₂×C₄²	Dic₁₅	1	4	yes	—
82	C₂×C₄²	C₂×D₁₅	1	2	yes	—
83	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
84	#97	—	15	16	no	—
85	C₄×C₈	—	15	8	no	—
86	C₂×C₃×C₅	C₄³	1	1	yes	characteristic
87	C₂×C₃×C₅	C₂×#97	1	2	yes	—
88	C₂×C₃×C₅	C₄×M₁₆	1	4	yes	—
89	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
90	C₂×C₃×C₄	—	2	8	no	—
91	C₂×C₃×C₄	#681	1	8	yes	—
92	C₂×C₃×C₄	C₄×Dic₅	1	8	yes	—
93	C₂×C₃×C₄	C₄×Dic₅	1	4	yes	—
94	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
95	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
96	C₃⋊C₈	—	5	16	no	—
97	C₂²×C₅	C₂×#208	1	4	yes	—
98	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
99	C₂²×C₅	C₂×C₄×Dic₃	1	2	yes	—
100	C₄×C₅	—	2	8	no	—
101	C₄×C₅	#803	1	8	yes	complemented
102	C₄×C₅	C₄²×D₃	1	4	yes	—
103	C₂²×C₄	C₂×Dic₁₅	1	4	yes	—
104	C₂²×C₄	C₂×Dic₁₅	1	2	yes	—
105	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
106	C₂×C₈	—	15	8	no	—
107	C₂×C₈	—	15	16	no	—
108	C₄²	—	2	8	no	—
109	C₄²	C₄×D₁₅	1	4	yes	—
110	C₄²	C₄×D₁₅	1	8	yes	—
111	C₃×C₅	C₄×#97	1	1	yes	characteristic, complemented, Hall
112	C₂²×C₃	C₂×#681	1	4	yes	—
113	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
114	C₂²×C₃	C₂×C₄×Dic₅	1	2	yes	—
115	C₃×C₄	—	2	8	no	—
116	C₃×C₄	#3935	1	8	yes	complemented
117	C₃×C₄	C₄²×D₅	1	4	yes	—
118	C₂×C₅	C₂×#803	1	2	yes	—
119	C₂×C₅	C₄×#208	1	4	yes	—
120	C₂×C₅	C₄²×Dic₃	1	1	yes	characteristic
121	C₂³	C₂²×Dic₁₅	1	1	yes	characteristic
122	C₂×C₄	—	2	8	no	—
123	C₂×C₄	#6710	1	8	yes	—
124	C₂×C₄	C₄×Dic₁₅	1	8	yes	—
125	C₂×C₄	C₄×Dic₁₅	1	4	yes	—
126	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
127	C₂×C₄	C₂×C₄×D₁₅	1	4	yes	—
128	C₈	—	15	16	no	—
129	C₂×C₃	C₂×#3935	1	2	yes	—
130	C₂×C₃	C₄×#681	1	4	yes	—
131	C₂×C₃	C₄²×Dic₅	1	1	yes	characteristic
132	C₅	C₄×#803	1	1	yes	characteristic, complemented, Sylow
133	C₂²	C₂×#6710	1	4	yes	—
134	C₂²	C₂×C₄×Dic₁₅	1	1	yes	characteristic
135	C₂²	C₂×C₄×Dic₁₅	1	2	yes	—
136	C₄	—	2	8	no	—
137	C₄	#91087	1	8	yes	direct product factor
138	C₄	C₄²×D₁₅	1	4	yes	—
139	C₃	C₄×#3935	1	1	yes	characteristic, complemented, Sylow
140	C₂	C₂×#91087	1	2	yes	—
141	C₂	C₄×#6710	1	4	yes	—
142	C₂	C₄²×Dic₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂×D₁₅
commutator	C₂×C₃×C₅	C₄³
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₃×C₄³×C₅	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₄³	D₁₅
hypocenter	C₃×C₅	C₄×#97
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄² ◁ C₄³

Complements

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

N	H ≅ G/N	type
9. #91087	C₄	direct (N × H)
10. C₄×C₃⋊#168	C₄	semidirect
40. C₃⋊#168	C₄²	semidirect
62. C₃×C₄×C₅	#97	semidirect
101. C₄×C₅	#803	semidirect
111. C₃×C₅	C₄×#97	semidirect
116. C₃×C₄	#3935	semidirect
132. C₅	C₄×#803	semidirect
137. C₄	#91087	direct (N × H)
139. C₃	C₄×#3935	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₄³×C₅	2
C₂×#91087	2
C₂×C₄×C₃⋊#168	2
C₄×#3935	3
C₄×#803	5

Subgroups — C4×#91087 #14294208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#91087 #14294208