Subgroups — #14294911

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91087	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
4	#11745966	C₂	1	4	yes	maximal
5	#10600598	—	3	1	no	maximal, Hall
6	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂²×C₃⋊#168	C₂²	1	2	yes	—
8	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₄×Dic₅	C₄	1	4	yes	—
10	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
11	#91087	C₄	1	4	yes	complemented
12	C₅×#803	C₄	1	4	yes	complemented
13	#69389	—	5	1	no	maximal, Hall
14	C₂×C₅×#97	—	3	1	no	—
15	C₄²×Dic₅	D₃	1	1	yes	characteristic
16	C₂×#3935	—	3	1	no	—
17	#64770	—	3	4	no	—
18	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
19	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
20	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
21	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
22	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
23	C₂×C₃⋊#168	—	2	4	no	—
24	C₂×C₃⋊#168	C₂×C₄	1	4	yes	—
25	C₂×C₅×C₃⋊C₈	—	2	4	no	—
26	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
27	C₃×C₄×Dic₅	—	2	4	no	—
28	C₃×C₄×Dic₅	—	2	8	no	—
29	C₃×C₄³	—	5	1	no	—
30	C₂×#803	—	5	1	no	—
31	C₂×#803	D₅	1	1	yes	characteristic
32	#4524	—	5	4	no	—
33	C₂²×C₅×C₈	—	3	2	no	—
34	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
35	C₂×C₄×Dic₅	Dic₃	1	4	yes	—
36	C₂×C₄×Dic₅	C₂×D₃	1	2	yes	—
37	C₂²×#168	—	3	2	no	—
38	C₅×#97	—	3	4	no	—
39	#3935	—	3	4	no	—
40	#1745	—	15	1	no	Sylow
41	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×C₅	—	2	4	no	—
43	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
44	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₅	#41	1	4	yes	—
47	C₂×C₃×Dic₅	—	2	4	no	—
48	C₂×C₃×Dic₅	—	2	4	no	—
49	C₂×C₃×Dic₅	M₁₆	1	8	yes	—
50	C₃⋊#168	—	2	4	no	—
51	C₅×C₃⋊C₈	—	2	4	no	—
52	C₂×C₃×C₄²	—	5	4	no	—
53	C₂×C₃×C₄²	—	5	2	no	—
54	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
55	C₂²×C₃⋊C₈	—	5	2	no	—
56	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
57	#803	—	5	4	no	—
58	#803	Dic₅	1	4	yes	complemented
59	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
60	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
61	C₂²×Dic₅	C₂×Dic₃	1	4	yes	—
62	C₂×C₅×C₈	—	3	4	no	—
63	C₂×C₅×C₈	—	6	4	no	—
64	C₄²×C₅	C₄×D₃	1	2	yes	—
65	C₄²×C₅	C₄×D₃	1	2	yes	—
66	C₄×Dic₅	—	2	4	no	—
67	C₄×Dic₅	—	2	8	no	—
68	C₂×#168	—	3	4	no	—
69	C₂×#168	—	6	4	no	—
70	C₂×#97	—	3	1	no	—
71	C₂×#97	—	15	1	no	—
72	C₄³	—	5	1	no	—
73	#336	—	15	4	no	—
74	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
75	C₂²×C₃×C₅	#117	1	2	yes	—
76	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	—
77	C₃×C₄×C₅	—	2	4	no	—
78	C₃×C₄×C₅	#117	1	2	yes	—
79	C₃×C₄×C₅	#117	1	2	yes	—
80	C₃×Dic₅	—	2	8	no	—
81	C₂²×C₃×C₄	—	5	4	no	—
82	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
83	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
84	C₃×C₄²	—	10	8	no	—
85	C₃×C₄²	—	10	4	no	—
86	C₃×C₄²	C₄×D₅	1	2	yes	—
87	C₃×C₄²	C₂×Dic₅	1	2	yes	—
88	C₂×C₃⋊C₈	—	2	4	no	—
89	C₂×C₃⋊C₈	—	5	4	no	—
90	C₂×C₃⋊C₈	—	10	4	no	—
91	C₂×C₃⋊C₈	C₂×Dic₅	1	4	yes	—
92	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
93	C₂×C₄×C₅	—	2	4	no	—
94	C₂×C₄×C₅	C₄×Dic₃	1	4	yes	—
95	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
96	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
97	C₂×C₄×C₅	#235	1	4	yes	—
98	C₂×Dic₅	—	2	4	no	—
99	C₂×Dic₅	—	2	4	no	—
100	C₂×Dic₅	#208	1	8	yes	—
101	C₅×C₈	—	6	4	no	—
102	#168	—	6	4	no	—
103	C₂²×C₈	—	3	2	no	—
104	C₂²×C₈	—	15	2	no	—
105	C₂×C₄²	—	5	4	no	—
106	C₂×C₄²	—	5	2	no	—
107	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
108	#97	—	3	4	no	—
109	#97	—	15	4	no	—
110	C₂×C₃×C₅	#376	1	1	yes	characteristic
111	C₂×C₃×C₅	C₄×M₁₆	1	2	yes	—
112	C₂×C₃×C₅	#432	1	4	yes	—
113	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
114	C₂×C₃×C₄	—	2	4	no	—
115	C₂×C₃×C₄	—	5	8	no	—
116	C₂×C₃×C₄	—	10	4	no	—
117	C₂×C₃×C₄	—	10	4	no	—
118	C₂×C₃×C₄	C₄×Dic₅	1	4	yes	—
119	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
120	C₂×C₃×C₄	#709	1	4	yes	—
121	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
122	C₃⋊C₈	—	2	4	no	—
123	C₃⋊C₈	—	10	4	no	—
124	C₂²×C₅	C₂×#208	1	4	yes	—
125	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
126	C₂²×C₅	#926	1	2	yes	—
127	C₄×C₅	—	2	4	no	—
128	C₄×C₅	#872	1	2	yes	—
129	C₄×C₅	#872	1	2	yes	—
130	Dic₅	—	2	8	no	—
131	C₂²×C₄	—	5	4	no	—
132	C₂²×C₄	D₅×Dic₃	1	2	yes	—
133	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
134	C₂×C₈	—	3	4	no	—
135	C₂×C₈	—	6	4	no	—
136	C₂×C₈	—	15	4	no	—
137	C₂×C₈	—	30	4	no	—
138	C₄²	—	10	8	no	—
139	C₄²	—	10	4	no	—
140	C₄²	D₃×Dic₅	1	2	yes	—
141	C₄²	#1200	1	2	yes	—
142	C₃×C₅	#1745	1	1	yes	characteristic, complemented, Hall
143	C₂²×C₃	#4018	1	2	yes	—
144	C₂²×C₃	D₅×M₁₆	1	4	yes	—
145	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
146	C₃×C₄	—	2	4	no	—
147	C₃×C₄	—	10	8	no	—
148	C₃×C₄	#4018	1	2	yes	—
149	C₃×C₄	#4072	1	2	yes	—
150	C₂×C₅	C₄×#208	1	2	yes	—
151	C₂×C₅	#4926	1	4	yes	—
152	C₂×C₅	#4932	1	1	yes	characteristic
153	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	5	8	no	—
156	C₂×C₄	—	10	4	no	—
157	C₂×C₄	—	10	4	no	—
158	C₂×C₄	Dic₃×Dic₅	1	4	yes	—
159	C₂×C₄	#6771	1	4	yes	—
160	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
161	C₂×C₄	C₂×#1200	1	1	yes	characteristic
162	C₈	—	6	4	no	—
163	C₈	—	30	4	no	—
164	C₂×C₃	#64994	1	4	yes	—
165	C₂×C₃	#65221	1	1	yes	characteristic
166	C₂×C₃	M₁₆×Dic₅	1	2	yes	—
167	C₅	#69389	1	1	yes	characteristic, complemented, Sylow
168	C₂²	D₅×#208	1	4	yes	—
169	C₂²	#91357	1	2	yes	—
170	C₂²	C₂×Dic₃×Dic₅	1	1	yes	characteristic
171	C₄	—	2	4	no	—
172	C₄	—	10	8	no	—
173	C₄	#91371	1	2	yes	—
174	C₄	#91386	1	2	yes	—
175	C₃	#10600598	1	1	yes	characteristic, complemented, Sylow
176	C₂	#11746870	1	4	yes	—
177	C₂	Dic₅×#208	1	2	yes	—
178	C₂	#11748611	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1745
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
11. #91087	C₄	semidirect
12. C₅×#803	C₄	semidirect
58. #803	Dic₅	semidirect
142. C₃×C₅	#1745	semidirect
167. C₅	#69389	semidirect
175. C₃	#10600598	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91087	2
C₂×C₅×#803	2
C₃×C₄²×Dic₅	2
#11745966	2
#10600598	3
#69389	5