Subgroups — #14294913

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	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3935	C₂	1	1	yes	maximal, characteristic
4	#11745967	C₂	1	4	yes	maximal
5	#10600182	—	3	1	no	maximal, Hall
6	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂²×C₃⋊#168	C₂²	1	2	yes	—
8	C₂×C₄×C₅×Dic₃	C₄	1	4	yes	—
9	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
10	C₂²×C₃×#168	C₂²	1	2	yes	—
11	#91087	C₄	1	4	yes	complemented
12	C₃×#3935	C₄	1	4	yes	complemented
13	#69805	—	5	1	no	maximal, Hall
14	C₄³×C₅	—	3	1	no	—
15	C₂×#3935	—	3	1	no	—
16	C₂×#3935	D₃	1	1	yes	characteristic
17	#64744	—	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×C₅×Dic₃	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	C₄×C₅×Dic₃	—	2	4	no	—
26	C₄×C₅×Dic₃	—	2	8	no	—
27	C₂×C₃×#168	—	2	4	no	—
28	C₂×C₃×#168	C₂×C₄	1	4	yes	—
29	C₂×C₃×#97	—	5	1	no	—
30	C₄²×Dic₃	D₅	1	1	yes	characteristic
31	C₂×#803	—	5	1	no	—
32	#4550	—	5	4	no	—
33	C₂×C₄²×C₅	—	3	4	no	—
34	C₂×C₄²×C₅	—	3	2	no	—
35	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
36	C₂²×#168	—	3	2	no	—
37	C₂²×#168	C₂×D₃	1	2	yes	—
38	#3935	—	3	4	no	—
39	#3935	Dic₃	1	4	yes	complemented
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×C₅×Dic₃	—	2	4	no	—
48	C₂×C₅×Dic₃	—	2	4	no	—
49	C₂×C₅×Dic₃	M₁₆	1	8	yes	—
50	C₃⋊#168	—	2	4	no	—
51	C₃×#168	—	2	4	no	—
52	C₂²×C₃×C₈	—	5	2	no	—
53	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
54	C₂×C₄×Dic₃	Dic₅	1	4	yes	—
55	C₂×C₄×Dic₃	C₂×D₅	1	2	yes	—
56	C₂²×C₃⋊C₈	—	5	2	no	—
57	C₃×#97	—	5	4	no	—
58	#803	—	5	4	no	—
59	C₂²×C₄×C₅	—	3	4	no	—
60	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
61	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
62	C₄²×C₅	—	6	8	no	—
63	C₄²×C₅	—	6	4	no	—
64	C₄²×C₅	C₄×D₃	1	2	yes	—
65	C₄²×C₅	C₂×Dic₃	1	2	yes	—
66	C₂×#168	—	2	4	no	—
67	C₂×#168	—	3	4	no	—
68	C₂×#168	—	6	4	no	—
69	C₂×#168	C₂×Dic₃	1	4	yes	—
70	C₂×#97	—	5	1	no	—
71	C₂×#97	—	15	1	no	—
72	C₄³	—	3	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	C₅×Dic₃	—	2	8	no	—
81	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
82	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
83	C₂²×Dic₃	C₂×Dic₅	1	4	yes	—
84	C₂×C₃×C₈	—	5	4	no	—
85	C₂×C₃×C₈	—	10	4	no	—
86	C₃×C₄²	C₄×D₅	1	2	yes	—
87	C₃×C₄²	C₄×D₅	1	2	yes	—
88	C₄×Dic₃	—	2	4	no	—
89	C₄×Dic₃	—	2	8	no	—
90	C₂×C₃⋊C₈	—	5	4	no	—
91	C₂×C₃⋊C₈	—	10	4	no	—
92	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
93	C₂×C₄×C₅	—	2	4	no	—
94	C₂×C₄×C₅	—	3	8	no	—
95	C₂×C₄×C₅	—	6	4	no	—
96	C₂×C₄×C₅	—	6	4	no	—
97	C₂×C₄×C₅	C₄×Dic₃	1	4	yes	—
98	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
99	C₂×C₄×C₅	#235	1	4	yes	—
100	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
101	#168	—	2	4	no	—
102	#168	—	6	4	no	—
103	C₂²×C₈	—	5	2	no	—
104	C₂²×C₈	—	15	2	no	—
105	C₂×C₄²	—	3	4	no	—
106	C₂×C₄²	—	3	2	no	—
107	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
108	#97	—	5	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	C₂²×Dic₅	1	1	yes	characteristic
114	C₂×C₃×C₄	—	2	4	no	—
115	C₂×C₃×C₄	C₄×Dic₅	1	4	yes	—
116	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
117	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
118	C₂×C₃×C₄	#709	1	4	yes	—
119	C₂×Dic₃	—	2	4	no	—
120	C₂×Dic₃	—	2	4	no	—
121	C₂×Dic₃	#681	1	8	yes	—
122	C₃×C₈	—	10	4	no	—
123	C₃⋊C₈	—	10	4	no	—
124	C₂²×C₅	#872	1	2	yes	—
125	C₂²×C₅	D₃×M₁₆	1	4	yes	—
126	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
127	C₄×C₅	—	2	4	no	—
128	C₄×C₅	—	6	8	no	—
129	C₄×C₅	#872	1	2	yes	—
130	C₄×C₅	#926	1	2	yes	—
131	C₂²×C₄	—	3	4	no	—
132	C₂²×C₄	D₃×Dic₅	1	2	yes	—
133	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
134	C₂×C₈	—	5	4	no	—
135	C₂×C₈	—	10	4	no	—
136	C₂×C₈	—	15	4	no	—
137	C₂×C₈	—	30	4	no	—
138	C₄²	—	6	8	no	—
139	C₄²	—	6	4	no	—
140	C₄²	D₅×Dic₃	1	2	yes	—
141	C₄²	#1200	1	2	yes	—
142	C₃×C₅	#1745	1	1	yes	characteristic, complemented, Hall
143	C₂²×C₃	C₂×#681	1	4	yes	—
144	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
145	C₂²×C₃	#4072	1	2	yes	—
146	C₃×C₄	—	2	4	no	—
147	C₃×C₄	#4018	1	2	yes	—
148	C₃×C₄	#4018	1	2	yes	—
149	Dic₃	—	2	8	no	—
150	C₂×C₅	#4705	1	4	yes	—
151	C₂×C₅	#4932	1	1	yes	characteristic
152	C₂×C₅	Dic₃×M₁₆	1	2	yes	—
153	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	3	8	no	—
156	C₂×C₄	—	6	4	no	—
157	C₂×C₄	—	6	4	no	—
158	C₂×C₄	Dic₃×Dic₅	1	4	yes	—
159	C₂×C₄	#6771	1	4	yes	—
160	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
161	C₂×C₄	C₂×#1200	1	1	yes	characteristic
162	C₈	—	10	4	no	—
163	C₈	—	30	4	no	—
164	C₂×C₃	C₄×#681	1	2	yes	—
165	C₂×C₃	#65215	1	4	yes	—
166	C₂×C₃	#65221	1	1	yes	characteristic
167	C₅	#69805	1	1	yes	characteristic, complemented, Sylow
168	C₂²	D₃×#681	1	4	yes	—
169	C₂²	#91371	1	2	yes	—
170	C₂²	C₂×Dic₃×Dic₅	1	1	yes	characteristic
171	C₄	—	2	4	no	—
172	C₄	—	6	8	no	—
173	C₄	#91357	1	2	yes	—
174	C₄	#91386	1	2	yes	—
175	C₃	#10600182	1	1	yes	characteristic, complemented, Sylow
176	C₂	#11746878	1	4	yes	—
177	C₂	Dic₃×#681	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. C₃×#3935	C₄	semidirect
39. #3935	Dic₃	semidirect
142. C₃×C₅	#1745	semidirect
167. C₅	#69805	semidirect
175. C₃	#10600182	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
C₄²×C₅×Dic₃	2
C₂×C₃×#3935	2
#11745967	2
#10600182	3
#69805	5