Subgroups — C₃×#10598152 #14276834

Order 1920.

304 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic
2	C₃×#65214	C₂	1	2	yes	maximal
3	#10598152	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅×C₈	C₄	1	2	yes	—
5	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
6	C₃×C₅×#97	—	2	2	no	—
7	C₃×C₂²⋊#168	C₄	1	4	yes	—
8	C₃×C₄⋊#168	—	2	2	no	—
9	C₃×C₄×#168	—	2	2	no	—
10	C₃×#1281	—	5	1	no	maximal, Hall
11	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic
12	#65214	C₂×C₃	1	2	yes	—
13	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
14	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×C₅×C₈	—	2	2	no	—
16	C₂×C₃×C₅×C₈	—	2	2	no	—
17	C₂×C₃×C₅×C₈	C₈	1	4	yes	complemented
18	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
19	C₃×C₄²×C₅	D₄	1	2	yes	—
20	C₃×C₄²×C₅	Q₈	1	1	yes	characteristic
21	C₂×C₃×#168	—	2	4	no	—
22	C₃×#431	—	5	2	no	—
23	C₂×C₃×#97	D₅	1	1	yes	characteristic
24	C₂²×C₅×C₈	C₃×C₄	1	2	yes	—
25	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
26	C₅×#97	—	2	2	no	—
27	C₂²⋊#168	C₃×C₄	1	4	yes	—
28	C₄⋊#168	—	2	2	no	—
29	C₄×#168	—	2	2	no	—
30	#1281	—	5	1	no	Sylow
31	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
32	C₂×C₃×C₄×C₅	—	4	2	no	—
33	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
34	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
36	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
38	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
39	C₃×C₅×C₈	—	2	4	no	—
40	C₃×#168	—	4	4	no	—
41	C₂²×C₃×C₈	Dic₅	1	2	yes	—
42	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
43	C₃×C₄⋊C₈	—	10	2	no	—
44	C₃×C₂²⋊C₈	—	5	4	no	—
45	C₃×#97	—	2	2	no	—
46	C₃×C₄×C₈	—	10	2	no	—
47	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
48	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	—	2	2	no	—
51	C₂×C₅×C₈	C₃×C₈	1	4	yes	complemented
52	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
53	C₄²×C₅	C₃×D₄	1	2	yes	—
54	C₄²×C₅	C₃×Q₈	1	1	yes	characteristic
55	C₂×#168	—	2	4	no	—
56	#431	—	5	2	no	—
57	C₂×#97	C₃×D₅	1	1	yes	characteristic
58	C₂²×C₃×C₅	—	2	2	no	—
59	C₂²×C₃×C₅	#95	1	1	yes	characteristic
60	C₂²×C₃×C₅	C₄×C₈	1	1	yes	characteristic
61	C₂²×C₃×C₅	#97	1	1	yes	characteristic
62	C₃×C₄×C₅	—	2	2	no	—
63	C₃×C₄×C₅	—	2	2	no	—
64	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
65	C₃×C₄×C₅	C₄⋊C₈	1	2	yes	—
66	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
67	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
68	C₂×C₃×C₈	—	2	2	no	—
69	C₂×C₃×C₈	—	2	2	no	—
70	C₂×C₃×C₈	—	10	4	no	—
71	C₂×C₃×C₈	#168	1	4	yes	complemented
72	C₃×C₄²	Dic₁₀	1	1	yes	characteristic
73	C₃×C₄²	D₂₀	1	1	yes	characteristic
74	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
75	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₅	—	4	2	no	—
77	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
78	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
80	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
82	C₂×C₄×C₅	C₃×M₁₆	1	2	yes	—
83	C₅×C₈	—	2	4	no	—
84	#168	—	4	4	no	—
85	C₂²×C₈	C₃×Dic₅	1	2	yes	—
86	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
87	C₄⋊C₈	—	10	2	no	—
88	C₂²⋊C₈	—	5	4	no	—
89	#97	—	2	2	no	—
90	C₄×C₈	—	10	2	no	—
91	C₂×C₃×C₅	—	2	1	no	—
92	C₂×C₃×C₅	—	2	1	no	—
93	C₂×C₃×C₅	#336	1	1	yes	characteristic
94	C₂×C₃×C₅	#344	1	2	yes	—
95	C₂³×C₃	C₄×Dic₅	1	1	yes	characteristic
96	C₂×C₃×C₄	—	4	2	no	—
97	C₂×C₃×C₄	C₂×#168	1	2	yes	—
98	C₂×C₃×C₄	#681	1	2	yes	—
99	C₂×C₃×C₄	#683	1	2	yes	—
100	C₂×C₃×C₄	C₄⋊Dic₅	1	1	yes	characteristic
101	C₂×C₃×C₄	#685	1	2	yes	—
102	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
103	C₃×C₈	—	2	4	no	—
104	C₃×C₈	—	20	4	no	—
105	C₂²×C₅	—	2	2	no	—
106	C₂²×C₅	C₃×#95	1	1	yes	characteristic
107	C₂²×C₅	C₃×C₄×C₈	1	1	yes	characteristic
108	C₂²×C₅	C₃×#97	1	1	yes	characteristic
109	C₄×C₅	—	2	2	no	—
110	C₄×C₅	—	2	2	no	—
111	C₄×C₅	C₃×C₂²⋊C₈	1	2	yes	—
112	C₄×C₅	C₃×C₄⋊C₈	1	2	yes	—
113	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
114	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	10	4	no	—
118	C₂×C₈	C₃×#168	1	4	yes	complemented
119	C₄²	C₃×Dic₁₀	1	1	yes	characteristic
120	C₄²	C₃×D₂₀	1	1	yes	characteristic
121	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
122	C₃×C₅	#1281	1	1	yes	characteristic, complemented, Hall
123	C₂²×C₃	—	2	2	no	—
124	C₂²×C₃	C₄×#168	1	1	yes	characteristic
125	C₂²×C₃	#3935	1	1	yes	characteristic
126	C₂²×C₃	#3963	1	1	yes	characteristic
127	C₃×C₄	—	2	2	no	—
128	C₃×C₄	—	2	2	no	—
129	C₃×C₄	C₄⋊#168	1	2	yes	—
130	C₃×C₄	C₂²⋊#168	1	2	yes	—
131	C₂×C₅	—	2	1	no	—
132	C₂×C₅	—	2	1	no	—
133	C₂×C₅	C₃×#336	1	1	yes	characteristic
134	C₂×C₅	C₃×#344	1	2	yes	—
135	C₂³	C₃×C₄×Dic₅	1	1	yes	characteristic
136	C₂×C₄	—	4	2	no	—
137	C₂×C₄	C₂×C₃×#168	1	2	yes	—
138	C₂×C₄	C₃×#681	1	2	yes	—
139	C₂×C₄	C₃×#683	1	2	yes	—
140	C₂×C₄	C₃×C₄⋊Dic₅	1	1	yes	characteristic
141	C₂×C₄	C₃×#685	1	2	yes	—
142	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
143	C₈	—	2	4	no	—
144	C₈	—	20	4	no	—
145	C₂×C₃	—	2	1	no	—
146	C₂×C₃	—	2	1	no	—
147	C₂×C₃	#64744	1	1	yes	characteristic
148	C₂×C₃	#64776	1	2	yes	—
149	C₅	C₃×#1281	1	1	yes	characteristic, complemented, Sylow
150	C₂²	—	2	2	no	—
151	C₂²	C₃×C₄×#168	1	1	yes	characteristic
152	C₂²	C₃×#3935	1	1	yes	characteristic
153	C₂²	C₃×#3963	1	1	yes	characteristic
154	C₄	—	2	2	no	—
155	C₄	—	2	2	no	—
156	C₄	C₃×C₄⋊#168	1	2	yes	—
157	C₄	C₃×C₂²⋊#168	1	2	yes	—
158	C₃	#10598152	1	1	yes	characteristic, direct product factor, Sylow
159	C₂	—	2	1	no	—
160	C₂	—	2	1	no	—
161	C₂	C₃×#64744	1	1	yes	characteristic
162	C₂	C₃×#64776	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²⋊Dic₅
commutator	C₂²×C₅	C₃×C₄×C₈
Frattini	C₂×C₄²	C₂×C₃×D₅
Fitting	C₂×C₃×C₅×#97	C₂
socle	C₂²×C₃×C₅	#95
prime radical	C₂³×C₃×C₅	C₄²
cosocle	C₂×C₄²×C₅	C₂²×C₃
hypercenter	C₂×C₃×#97	D₅
hypocenter	C₅	C₃×#1281
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
3. #10598152	C₃	direct (N × H)
17. C₂×C₃×C₅×C₈	C₈	semidirect
51. C₂×C₅×C₈	C₃×C₈	semidirect
71. C₂×C₃×C₈	#168	semidirect
118. C₂×C₈	C₃×#168	semidirect
122. C₃×C₅	#1281	semidirect
149. C₅	C₃×#1281	semidirect
158. C₃	#10598152	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×#97	2
C₃×#65214	2
#10598152	3
C₃×#1281	5

Subgroups — C3×#10598152 #14276834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10598152 #14276834