Subgroups — #14277099

Order 1920.

304 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#11751025	C₂	1	2	yes	maximal
3	#10598196	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅×C₈	C₄	1	2	yes	—
5	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
6	C₂×#6710	—	2	2	no	—
7	C₃×C₅×C₄⋊C₈	—	2	2	no	—
8	C₄⋊(C₃⋊#168)	—	2	2	no	—
9	C₄⋊(C₃⋊#168)	C₄	1	4	yes	—
10	#67705	—	5	1	no	maximal, Hall
11	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic
12	#65213	—	3	2	no	—
13	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₅	Q₈	1	1	yes	characteristic
16	C₂×C₃×C₅×C₈	—	2	2	no	—
17	C₂×C₃×C₅×C₈	—	4	2	no	—
18	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
19	C₃×C₄²×C₅	D₄	1	2	yes	—
20	#6710	—	4	2	no	—
21	#6710	—	4	2	no	—
22	C₂×C₃⋊#168	—	2	4	no	—
23	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic
24	#4924	—	5	2	no	—
25	C₂²×C₅×C₈	Dic₃	1	2	yes	—
26	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
27	C₂×#681	—	6	2	no	—
28	C₅×C₄⋊C₈	—	2	2	no	—
29	C₄⋊#168	—	3	4	no	—
30	C₄⋊#168	—	6	2	no	—
31	#1292	—	15	1	no	Sylow
32	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₃×C₄×C₅	—	2	1	no	—
34	C₂×C₃×C₄×C₅	—	2	1	no	—
35	C₂×C₃×C₄×C₅	—	4	1	no	—
36	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
37	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
39	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
40	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
41	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
42	C₂×C₃×C₄×C₅	Q₁₆	1	1	yes	characteristic
43	C₃×C₅×C₈	—	4	2	no	—
44	C₃⋊#168	—	4	4	no	—
45	C₂²×C₃×C₈	Dic₅	1	2	yes	—
46	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
47	C₂×#208	—	10	2	no	—
48	C₃×C₄⋊C₈	—	2	2	no	—
49	C₄⋊(C₃⋊C₈)	—	5	4	no	—
50	C₄⋊(C₃⋊C₈)	—	10	2	no	—
51	C₂²×C₄×C₅	Dic₆	1	1	yes	characteristic
52	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
53	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
54	C₂×C₅×C₈	—	2	2	no	—
55	C₂×C₅×C₈	—	4	2	no	—
56	C₄²×C₅	C₄×D₃	1	2	yes	—
57	C₄²×C₅	#67	1	2	yes	—
58	#681	—	12	2	no	—
59	#681	—	12	2	no	—
60	C₂×#168	—	6	4	no	—
61	#423	—	15	2	no	—
62	C₂×C₄⋊C₈	D₁₅	1	1	yes	characteristic
63	C₂²×C₃×C₅	—	2	1	no	—
64	C₂²×C₃×C₅	—	2	1	no	—
65	C₂²×C₃×C₅	#95	1	1	yes	characteristic
66	C₂²×C₃×C₅	#106	1	1	yes	characteristic
67	C₂²×C₃×C₅	#107	1	1	yes	characteristic
68	C₃×C₄×C₅	—	2	2	no	—
69	C₃×C₄×C₅	—	2	1	no	—
70	C₃×C₄×C₅	#100	1	1	yes	characteristic
71	C₃×C₄×C₅	#101	1	1	yes	characteristic
72	C₃×C₄×C₅	#102	1	2	yes	—
73	C₃×C₄×C₅	#103	1	2	yes	—
74	C₂²×C₃×C₄	Dic₁₀	1	1	yes	characteristic
75	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
76	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
77	C₂×C₃×C₈	—	2	2	no	—
78	C₂×C₃×C₈	—	4	2	no	—
79	C₃×C₄²	C₄×D₅	1	2	yes	—
80	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
81	#208	—	20	2	no	—
82	#208	—	20	2	no	—
83	C₂×C₃⋊C₈	—	10	4	no	—
84	C₂³×C₅	C₄⋊Dic₃	1	1	yes	characteristic
85	C₂×C₄×C₅	—	2	1	no	—
86	C₂×C₄×C₅	—	2	1	no	—
87	C₂×C₄×C₅	—	4	1	no	—
88	C₂×C₄×C₅	#204	1	2	yes	—
89	C₂×C₄×C₅	D₂₄	1	1	yes	characteristic
90	C₂×C₄×C₅	Dic₁₂	1	1	yes	characteristic
91	C₂×C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
92	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
93	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
94	C₂×C₄×C₅	#217	1	1	yes	characteristic
95	C₅×C₈	—	4	2	no	—
96	#168	—	12	4	no	—
97	C₂×M₁₆	—	30	2	no	—
98	C₂²×C₈	Dic₁₅	1	2	yes	—
99	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
100	C₄⋊C₈	—	2	2	no	—
101	C₄⋊C₈	—	15	4	no	—
102	C₄⋊C₈	—	30	2	no	—
103	C₂×C₃×C₅	—	2	1	no	—
104	C₂×C₃×C₅	—	2	1	no	—
105	C₂×C₃×C₅	#338	1	1	yes	characteristic
106	C₂×C₃×C₅	#340	1	1	yes	characteristic
107	C₂×C₃×C₅	#343	1	1	yes	characteristic
108	C₂³×C₃	C₄⋊Dic₅	1	1	yes	characteristic
109	C₂×C₃×C₄	—	2	1	no	—
110	C₂×C₃×C₄	—	2	1	no	—
111	C₂×C₃×C₄	—	4	1	no	—
112	C₂×C₃×C₄	#677	1	2	yes	—
113	C₂×C₃×C₄	D₄₀	1	1	yes	characteristic
114	C₂×C₃×C₄	Dic₂₀	1	1	yes	characteristic
115	C₂×C₃×C₄	C₄×Dic₅	1	1	yes	characteristic
116	C₂×C₃×C₄	#683	1	2	yes	—
117	C₂×C₃×C₄	#685	1	2	yes	—
118	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
119	C₃×C₈	—	4	2	no	—
120	C₃⋊C₈	—	20	4	no	—
121	C₂²×C₅	—	2	1	no	—
122	C₂²×C₅	—	2	1	no	—
123	C₂²×C₅	#817	1	1	yes	characteristic
124	C₂²×C₅	#818	1	1	yes	characteristic
125	C₂²×C₅	C₃⋊#95	1	1	yes	characteristic
126	C₄×C₅	—	2	1	no	—
127	C₄×C₅	—	2	2	no	—
128	C₄×C₅	#816	1	2	yes	—
129	C₄×C₅	#821	1	2	yes	—
130	C₄×C₅	#833	1	1	yes	characteristic
131	C₄×C₅	#836	1	1	yes	characteristic
132	C₂²×C₄	Dic₃₀	1	1	yes	characteristic
133	C₂²×C₄	D₆₀	1	1	yes	characteristic
134	C₂²×C₄	C₂×Dic₁₅	1	1	yes	characteristic
135	M₁₆	—	60	2	no	—
136	M₁₆	—	60	2	no	—
137	C₂×C₈	—	2	2	no	—
138	C₂×C₈	—	4	2	no	—
139	C₂×C₈	—	30	4	no	—
140	C₄²	C₄×D₁₅	1	2	yes	—
141	C₄²	#1220	1	2	yes	—
142	C₃×C₅	#1292	1	1	yes	characteristic, complemented, Hall
143	C₂²×C₃	—	2	1	no	—
144	C₂²×C₃	—	2	1	no	—
145	C₂²×C₃	#3949	1	1	yes	characteristic
146	C₂²×C₃	#3950	1	1	yes	characteristic
147	C₂²×C₃	#3963	1	1	yes	characteristic
148	C₃×C₄	—	2	2	no	—
149	C₃×C₄	—	2	1	no	—
150	C₃×C₄	#3948	1	2	yes	—
151	C₃×C₄	#3953	1	2	yes	—
152	C₃×C₄	#3965	1	1	yes	characteristic
153	C₃×C₄	#3968	1	1	yes	characteristic
154	C₂×C₅	—	2	1	no	—
155	C₂×C₅	—	2	1	no	—
156	C₂×C₅	#4530	1	1	yes	characteristic
157	C₂×C₅	#4551	1	1	yes	characteristic
158	C₂×C₅	C₃⋊#338	1	1	yes	characteristic
159	C₂³	C₄⋊Dic₁₅	1	1	yes	characteristic
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	1	no	—
162	C₂×C₄	—	4	1	no	—
163	C₂×C₄	#6706	1	2	yes	—
164	C₂×C₄	D₁₂₀	1	1	yes	characteristic
165	C₂×C₄	Dic₆₀	1	1	yes	characteristic
166	C₂×C₄	C₄×Dic₁₅	1	1	yes	characteristic
167	C₂×C₄	#6712	1	2	yes	—
168	C₂×C₄	#6714	1	2	yes	—
169	C₂×C₄	#6719	1	1	yes	characteristic
170	C₈	—	4	2	no	—
171	C₈	—	60	4	no	—
172	C₂×C₃	—	2	1	no	—
173	C₂×C₃	—	2	1	no	—
174	C₂×C₃	#64750	1	1	yes	characteristic
175	C₂×C₃	#64771	1	1	yes	characteristic
176	C₂×C₃	#64780	1	1	yes	characteristic
177	C₅	#67705	1	1	yes	characteristic, complemented, Sylow
178	C₂²	—	2	1	no	—
179	C₂²	—	2	1	no	—
180	C₂²	#91101	1	1	yes	characteristic
181	C₂²	#91102	1	1	yes	characteristic
182	C₂²	#91115	1	1	yes	characteristic
183	C₄	—	2	1	no	—
184	C₄	—	2	2	no	—
185	C₄	#91100	1	2	yes	—
186	C₄	#91105	1	2	yes	—
187	C₄	#91117	1	1	yes	characteristic
188	C₄	#91120	1	1	yes	characteristic
189	C₃	#10598196	1	1	yes	characteristic, complemented, Sylow
190	C₂	—	2	1	no	—
191	C₂	—	2	1	no	—
192	C₂	#11746351	1	1	yes	characteristic
193	C₂	#11746372	1	1	yes	characteristic
194	C₂	#11746381	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#91115
commutator	C₂×C₃×C₄×C₅	C₄²
Frattini	C₂×C₄²	C₂×D₁₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂²×C₃×C₅	#95
prime radical	C₂³×C₃×C₅	C₄⋊C₄
cosocle	C₂×C₃×C₄²×C₅	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₅
hypocenter	C₃×C₅	#1292
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
142. C₃×C₅	#1292	semidirect
177. C₅	#67705	semidirect
189. C₃	#10598196	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×C₄⋊C₈	2
#11751025	2
#10598196	3
#67705	5