Subgroups — C₂×#11745873 #14312562

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊#672	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
4	#11745873	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64722	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
8	C₂²×C₃×#168	C₄	1	1	yes	characteristic
9	C₂×C₃⋊#672	C₄	1	4	yes	complemented
10	C₂×C₃⋊#672	C₂²	1	2	yes	—
11	C₂×C₅×C₃⋊C₁₆	C₄	1	4	yes	complemented
12	C₂×C₅×C₃⋊C₁₆	C₂²	1	2	yes	—
13	C₃×C₈×Dic₅	C₄	1	2	yes	—
14	C₃×C₈×Dic₅	C₂²	1	2	yes	—
15	C₂×#4461	—	5	1	no	maximal, Hall
16	C₂²×C₅×C₁₆	—	3	1	no	—
17	C₂×C₈×Dic₅	D₃	1	1	yes	characteristic
18	C₂²×#672	—	3	1	no	—
19	#64722	—	3	4	no	—
20	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₃×Dic₅	C₈	1	2	yes	—
22	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
24	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
25	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
26	C₃×C₄×Dic₅	C₈	1	2	yes	—
27	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
28	C₂×C₃×#168	C₈	1	4	yes	—
29	C₂×C₃×#168	C₂×C₄	1	2	yes	—
30	C₃⋊#672	C₂×C₄	1	4	yes	complemented
31	C₅×C₃⋊C₁₆	C₂×C₄	1	4	yes	complemented
32	C₂×C₃×C₄×C₈	—	5	1	no	—
33	C₂²×C₃⋊C₁₆	—	5	1	no	—
34	C₂²×C₃⋊C₁₆	D₅	1	1	yes	characteristic
35	#4461	—	5	4	no	—
36	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
37	C₂×C₄×Dic₅	Dic₃	1	1	yes	characteristic
38	C₂²×#168	Dic₃	1	1	yes	characteristic
39	C₂×C₅×C₁₆	—	3	4	no	—
40	C₂×C₅×C₁₆	—	3	2	no	—
41	C₈×Dic₅	Dic₃	1	2	yes	—
42	C₈×Dic₅	C₂×D₃	1	2	yes	—
43	C₂×#672	—	3	4	no	—
44	C₂×#672	—	3	2	no	—
45	C₂×#346	—	15	1	no	Sylow
46	C₂³×C₃×C₅	C₂×C₈	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
48	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
50	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₃×Dic₅	—	2	4	no	—
52	C₂×C₃×Dic₅	C₂×C₈	1	4	yes	—
53	C₃×C₅×C₈	C₄²	1	2	yes	—
54	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
55	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
56	C₃×#168	C₂×C₈	1	4	yes	—
57	C₂²×C₃×C₈	—	5	1	no	—
58	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
59	C₂×C₃×C₄²	—	5	1	no	—
60	C₃×C₄×C₈	—	5	2	no	—
61	C₃×C₄×C₈	—	5	2	no	—
62	C₂×C₃⋊C₁₆	—	5	4	no	—
63	C₂×C₃⋊C₁₆	—	5	2	no	—
64	C₂×C₃⋊C₁₆	Dic₅	1	4	yes	complemented
65	C₂×C₃⋊C₁₆	C₂×D₅	1	2	yes	—
66	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
67	C₂²×Dic₅	C₃⋊C₈	1	2	yes	—
68	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
69	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
70	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
71	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
72	C₄×Dic₅	C₃⋊C₈	1	2	yes	—
73	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
74	C₂×#168	C₃⋊C₈	1	4	yes	—
75	C₂×#168	C₂×Dic₃	1	2	yes	—
76	C₅×C₁₆	—	3	4	no	—
77	#672	—	3	4	no	—
78	C₂²×C₁₆	—	3	1	no	—
79	C₂²×C₁₆	—	15	1	no	—
80	C₂×C₄×C₈	—	5	1	no	—
81	#346	—	15	4	no	—
82	C₂²×C₃×C₅	C₄×C₈	1	2	yes	—
83	C₂²×C₃×C₅	M₃₂	1	4	yes	—
84	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
85	C₃×C₄×C₅	C₄×C₈	1	2	yes	—
86	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
87	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
88	C₃×Dic₅	—	2	4	no	—
89	C₂²×C₃×C₄	—	5	2	no	—
90	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
91	C₂×C₃×C₈	—	5	4	no	—
92	C₂×C₃×C₈	—	5	2	no	—
93	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
94	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
95	C₂×C₃×C₈	C₂×Dic₅	1	2	yes	—
96	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
97	C₃×C₄²	—	5	2	no	—
98	C₃×C₄²	—	5	2	no	—
99	C₃⋊C₁₆	—	5	4	no	—
100	C₃⋊C₁₆	C₂×Dic₅	1	4	yes	complemented
101	C₂³×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
102	C₂×C₄×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
103	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
104	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
105	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
106	C₂×Dic₅	—	2	4	no	—
107	C₂×Dic₅	C₂×C₃⋊C₈	1	4	yes	—
108	C₅×C₈	C₄×Dic₃	1	2	yes	—
109	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
110	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
111	#168	C₂×C₃⋊C₈	1	4	yes	—
112	C₂²×C₈	—	5	1	no	—
113	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
114	C₂×C₄²	—	5	1	no	—
115	C₂×C₁₆	—	3	4	no	—
116	C₂×C₁₆	—	3	2	no	—
117	C₂×C₁₆	—	15	4	no	—
118	C₂×C₁₆	—	15	2	no	—
119	C₄×C₈	—	5	2	no	—
120	C₄×C₈	—	5	2	no	—
121	C₂×C₃×C₅	#346	1	4	yes	complemented
122	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
123	C₂×C₃×C₅	C₂×M₃₂	1	2	yes	—
124	C₂³×C₃	C₈×D₅	1	1	yes	characteristic
125	C₂×C₃×C₄	—	5	4	no	—
126	C₂×C₃×C₄	—	10	4	no	—
127	C₂×C₃×C₄	C₈×D₅	1	1	yes	characteristic
128	C₂×C₃×C₄	C₈×D₅	1	2	yes	—
129	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
130	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
131	C₃×C₈	—	5	4	no	—
132	C₃×C₈	C₄×Dic₅	1	2	yes	—
133	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
134	C₃×C₈	C₂²×Dic₅	1	1	yes	characteristic
135	C₂²×C₅	C₄×C₃⋊C₈	1	2	yes	—
136	C₂²×C₅	#812	1	4	yes	—
137	C₂²×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
138	C₄×C₅	C₄×C₃⋊C₈	1	2	yes	—
139	C₄×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
140	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
141	Dic₅	—	2	4	no	—
142	C₂²×C₄	—	5	2	no	—
143	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
144	C₂×C₈	—	5	2	no	—
145	C₂×C₈	—	5	4	no	—
146	C₂×C₈	D₅×Dic₃	1	1	yes	characteristic
147	C₂×C₈	D₃×Dic₅	1	2	yes	—
148	C₂×C₈	#1200	1	2	yes	—
149	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
150	C₄²	—	5	2	no	—
151	C₄²	—	5	2	no	—
152	C₁₆	—	3	4	no	—
153	C₁₆	—	15	4	no	—
154	C₃×C₅	C₂×#346	1	1	yes	characteristic, complemented, Hall
155	C₂²×C₃	#3930	1	4	yes	—
156	C₂²×C₃	C₈×Dic₅	1	2	yes	—
157	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
158	C₃×C₄	—	10	4	no	—
159	C₃×C₄	C₈×Dic₅	1	2	yes	—
160	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
161	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
162	C₂×C₅	#4461	1	4	yes	complemented
163	C₂×C₅	C₂×C₄×C₃⋊C₈	1	1	yes	characteristic
164	C₂×C₅	C₂×#812	1	2	yes	—
165	C₂³	D₅×C₃⋊C₈	1	1	yes	characteristic
166	C₂×C₄	—	5	4	no	—
167	C₂×C₄	—	10	4	no	—
168	C₂×C₄	D₅×C₃⋊C₈	1	1	yes	characteristic
169	C₂×C₄	D₅×C₃⋊C₈	1	2	yes	—
170	C₂×C₄	Dic₃×Dic₅	1	2	yes	—
171	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
172	C₈	—	5	4	no	—
173	C₈	Dic₃×Dic₅	1	2	yes	—
174	C₈	C₂×D₃×Dic₅	1	1	yes	characteristic
175	C₈	C₂×#1200	1	1	yes	characteristic
176	C₂×C₃	#64722	1	4	yes	complemented
177	C₂×C₃	C₂×#3930	1	2	yes	—
178	C₂×C₃	C₂×C₈×Dic₅	1	1	yes	characteristic
179	C₅	C₂×#4461	1	1	yes	characteristic, complemented, Sylow
180	C₂²	#90934	1	4	yes	—
181	C₂²	Dic₅×C₃⋊C₈	1	2	yes	—
182	C₂²	C₂×D₅×C₃⋊C₈	1	1	yes	characteristic
183	C₄	—	10	4	no	—
184	C₄	Dic₅×C₃⋊C₈	1	2	yes	—
185	C₄	C₂×D₅×C₃⋊C₈	1	1	yes	characteristic
186	C₄	C₂×Dic₃×Dic₅	1	1	yes	characteristic
187	C₃	C₂×#64722	1	1	yes	characteristic, complemented, Sylow
188	C₂	#11745873	1	4	yes	direct product factor
189	C₂	C₂×#90934	1	2	yes	—
190	C₂	C₂×Dic₅×C₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	D₃×D₅
commutator	C₂×C₃×C₅	C₂×C₄×C₈
Frattini	C₂×C₈	C₂×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle, prime radical	C₂³×C₃×C₅	C₂×C₈
cosocle	C₂×C₃×C₅×C₈	C₂³
hypocenter	C₃×C₅	C₂×#346
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #11745873	C₂	direct (N × H)
9. C₂×C₃⋊#672	C₄	semidirect
11. C₂×C₅×C₃⋊C₁₆	C₄	semidirect
30. C₃⋊#672	C₂×C₄	semidirect
31. C₅×C₃⋊C₁₆	C₂×C₄	semidirect
64. C₂×C₃⋊C₁₆	Dic₅	semidirect
100. C₃⋊C₁₆	C₂×Dic₅	semidirect
121. C₂×C₃×C₅	#346	semidirect
154. C₃×C₅	C₂×#346	semidirect
162. C₂×C₅	#4461	semidirect
176. C₂×C₃	#64722	semidirect
179. C₅	C₂×#4461	semidirect
187. C₃	C₂×#64722	semidirect
188. C₂	#11745873	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃⋊#672	2
C₂²×C₅×C₃⋊C₁₆	2
C₂×C₃×C₈×Dic₅	2
#11745873	2
C₂×#64722	3
C₂×#4461	5

Subgroups — C2×#11745873 #14312562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745873 #14312562