Subgroups — C₂×#11745944 #14314581

Order 1920.

336 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91102	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3950	C₂	1	1	yes	maximal, characteristic
4	#11745944	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64725	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₁₅	—	2	1	no	—
8	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
9	#91102	—	2	1	no	—
10	#91102	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×#3950	—	2	1	no	—
14	C₃×#3950	C₂²	1	2	yes	—
15	C₂×#4490	—	5	1	no	maximal, Hall
16	C₂²×C₅×C₁₆	—	3	1	no	—
17	C₂×#3950	—	3	1	no	—
18	C₂×#3950	D₃	1	1	yes	characteristic
19	#64725	—	3	4	no	—
20	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
21	C₂²×Dic₁₅	—	4	1	no	—
22	C₂²×C₃×Dic₅	—	4	1	no	—
23	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
24	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
25	C₂×C₃×C₅×C₈	Q₈	1	2	yes	—
26	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₁₅	—	2	2	no	—
28	C₄⋊Dic₁₅	—	4	1	no	—
29	C₃×C₄⋊Dic₅	—	2	2	no	—
30	C₃×C₄⋊Dic₅	—	4	1	no	—
31	C₅×C₃⋊C₁₆	C₂×C₄	1	4	yes	complemented
32	C₂×C₃×#107	—	5	1	no	—
33	C₂×#818	—	5	1	no	—
34	C₂²×C₃⋊C₁₆	D₅	1	1	yes	characteristic
35	#4490	—	5	4	no	—
36	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
37	C₂×C₄⋊Dic₅	—	2	1	no	—
38	C₂×C₄⋊Dic₅	—	6	1	no	—
39	C₂×C₅×C₁₆	—	3	4	no	—
40	C₂×C₅×C₁₆	—	3	2	no	—
41	#3950	—	2	1	no	—
42	#3950	—	3	2	no	—
43	#3950	—	6	1	no	—
44	#3950	C₂×D₃	1	2	yes	—
45	C₂×#367	—	15	1	no	Sylow
46	C₂³×C₃×C₅	D₈	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
48	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	Q₁₆	1	2	yes	—
50	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₁₅	—	4	2	no	—
52	C₂×Dic₁₅	—	8	2	no	—
53	C₂×C₃×Dic₅	—	4	2	no	—
54	C₂×C₃×Dic₅	—	8	2	no	—
55	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
56	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
57	C₃×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
58	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
59	C₂×C₃×C₄⋊C₄	—	10	1	no	—
60	C₂×C₄⋊Dic₃	—	10	1	no	—
61	C₃×#107	—	5	2	no	—
62	C₃×#107	—	10	1	no	—
63	#818	—	5	2	no	—
64	#818	—	10	1	no	—
65	C₂×C₃⋊C₁₆	Dic₅	1	4	yes	complemented
66	C₂×C₃⋊C₁₆	C₂×D₅	1	2	yes	—
67	C₂²×C₄×C₅	#67	1	1	yes	characteristic
68	C₂²×Dic₅	—	4	1	no	—
69	C₂²×Dic₅	—	12	1	no	—
70	C₂×C₅×C₈	Dic₆	1	2	yes	—
71	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
72	C₂×C₅×C₈	#67	1	1	yes	characteristic
73	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
74	C₄⋊Dic₅	—	2	2	no	—
75	C₄⋊Dic₅	—	4	1	no	—
76	C₄⋊Dic₅	—	6	2	no	—
77	C₄⋊Dic₅	—	12	1	no	—
78	C₅×C₁₆	—	3	4	no	—
79	C₂²×C₁₆	—	3	1	no	—
80	C₂×#107	—	5	1	no	—
81	C₂×#107	—	15	1	no	—
82	#367	—	15	4	no	—
83	C₂²×C₃×C₅	#107	1	2	yes	—
84	C₂²×C₃×C₅	SD₃₂	1	2	yes	—
85	C₂²×C₃×C₅	SD₃₂	1	2	yes	—
86	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
87	C₃×C₄×C₅	#107	1	2	yes	—
88	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₃×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
90	Dic₁₅	—	8	2	no	—
91	C₃×Dic₅	—	8	2	no	—
92	C₂²×C₃×C₄	—	20	1	no	—
93	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
94	C₂²×Dic₃	—	20	1	no	—
95	C₂×C₃×C₈	Dic₁₀	1	2	yes	—
96	C₂×C₃×C₈	D₂₀	1	1	yes	characteristic
97	C₂×C₃×C₈	C₂×Dic₅	1	2	yes	—
98	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
99	C₃×C₄⋊C₄	—	10	2	no	—
100	C₃×C₄⋊C₄	—	20	1	no	—
101	C₄⋊Dic₃	—	10	2	no	—
102	C₄⋊Dic₃	—	20	1	no	—
103	C₃⋊C₁₆	C₂×Dic₅	1	4	yes	complemented
104	C₂³×C₅	#213	1	1	yes	characteristic
105	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
106	C₂×C₄×C₅	#213	1	1	yes	characteristic
107	C₂×C₄×C₅	#216	1	2	yes	—
108	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
109	C₂×Dic₅	—	4	2	no	—
110	C₂×Dic₅	—	8	2	no	—
111	C₂×Dic₅	—	12	2	no	—
112	C₂×Dic₅	—	24	2	no	—
113	C₅×C₈	Dic₃⋊C₄	1	2	yes	—
114	C₅×C₈	C₂×Dic₆	1	1	yes	characteristic
115	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
116	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
117	C₂×C₄⋊C₄	—	10	1	no	—
118	C₂×C₄⋊C₄	—	30	1	no	—
119	C₂×C₁₆	—	3	4	no	—
120	C₂×C₁₆	—	3	2	no	—
121	#107	—	5	2	no	—
122	#107	—	10	1	no	—
123	#107	—	15	2	no	—
124	#107	—	30	1	no	—
125	C₂×C₃×C₅	#367	1	4	yes	complemented
126	C₂×C₃×C₅	C₂×#107	1	1	yes	characteristic
127	C₂×C₃×C₅	C₂×SD₃₂	1	1	yes	characteristic
128	C₂×C₃×C₅	C₂×SD₃₂	1	1	yes	characteristic
129	C₂³×C₃	D₄₀	1	1	yes	characteristic
130	C₂×C₃×C₄	—	20	2	no	—
131	C₂×C₃×C₄	—	40	2	no	—
132	C₂×C₃×C₄	D₄₀	1	1	yes	characteristic
133	C₂×C₃×C₄	Dic₂₀	1	2	yes	—
134	C₂×C₃×C₄	C₄⋊Dic₅	1	2	yes	—
135	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
136	C₂×Dic₃	—	20	2	no	—
137	C₂×Dic₃	—	40	2	no	—
138	C₃×C₈	C₄⋊Dic₅	1	2	yes	—
139	C₃×C₈	C₂×Dic₁₀	1	1	yes	characteristic
140	C₃×C₈	C₂²×Dic₅	1	1	yes	characteristic
141	C₂²×C₅	#807	1	2	yes	—
142	C₂²×C₅	#827	1	2	yes	—
143	C₂²×C₅	#828	1	2	yes	—
144	C₂²×C₅	C₂×#213	1	1	yes	characteristic
145	C₄×C₅	#807	1	2	yes	—
146	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
147	C₄×C₅	C₂×#216	1	1	yes	characteristic
148	Dic₅	—	8	2	no	—
149	Dic₅	—	24	2	no	—
150	C₂²×C₄	—	20	1	no	—
151	C₂²×C₄	—	60	1	no	—
152	C₂²×C₄	#1202	1	1	yes	characteristic
153	C₂×C₈	D₃×Dic₅	1	2	yes	—
154	C₂×C₈	#1202	1	1	yes	characteristic
155	C₂×C₈	#1204	1	2	yes	—
156	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
157	C₄⋊C₄	—	10	2	no	—
158	C₄⋊C₄	—	20	1	no	—
159	C₄⋊C₄	—	30	2	no	—
160	C₄⋊C₄	—	60	1	no	—
161	C₁₆	—	3	4	no	—
162	C₃×C₅	C₂×#367	1	1	yes	characteristic, complemented, Hall
163	C₂²×C₃	#3932	1	2	yes	—
164	C₂²×C₃	#3932	1	2	yes	—
165	C₂²×C₃	#3950	1	2	yes	—
166	C₂²×C₃	C₂×D₄₀	1	1	yes	characteristic
167	C₃×C₄	—	40	2	no	—
168	C₃×C₄	#3950	1	2	yes	—
169	C₃×C₄	C₂×Dic₂₀	1	1	yes	characteristic
170	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
171	Dic₃	—	40	2	no	—
172	C₂×C₅	#4490	1	4	yes	complemented
173	C₂×C₅	C₂×#807	1	1	yes	characteristic
174	C₂×C₅	C₂×#827	1	1	yes	characteristic
175	C₂×C₅	C₂×#828	1	1	yes	characteristic
176	C₂³	#6653	1	1	yes	characteristic
177	C₂×C₄	—	20	2	no	—
178	C₂×C₄	—	40	2	no	—
179	C₂×C₄	—	60	2	no	—
180	C₂×C₄	—	120	2	no	—
181	C₂×C₄	#6653	1	1	yes	characteristic
182	C₂×C₄	#6662	1	2	yes	—
183	C₂×C₄	Dic₃⋊Dic₅	1	2	yes	—
184	C₂×C₄	C₂×#1202	1	1	yes	characteristic
185	C₈	Dic₃⋊Dic₅	1	2	yes	—
186	C₈	C₂×D₃×Dic₅	1	1	yes	characteristic
187	C₈	C₂×#1204	1	1	yes	characteristic
188	C₂×C₃	#64725	1	4	yes	complemented
189	C₂×C₃	C₂×#3932	1	1	yes	characteristic
190	C₂×C₃	C₂×#3932	1	1	yes	characteristic
191	C₂×C₃	C₂×#3950	1	1	yes	characteristic
192	C₅	C₂×#4490	1	1	yes	characteristic, complemented, Sylow
193	C₂²	#90942	1	2	yes	—
194	C₂²	#90943	1	2	yes	—
195	C₂²	#90990	1	2	yes	—
196	C₂²	C₂×#6653	1	1	yes	characteristic
197	C₄	—	40	2	no	—
198	C₄	—	120	2	no	—
199	C₄	#90990	1	2	yes	—
200	C₄	C₂×#6662	1	1	yes	characteristic
201	C₄	C₂×Dic₃⋊Dic₅	1	1	yes	characteristic
202	C₃	C₂×#64725	1	1	yes	characteristic, complemented, Sylow
203	C₂	#11745944	1	4	yes	direct product factor
204	C₂	C₂×#90942	1	1	yes	characteristic
205	C₂	C₂×#90943	1	1	yes	characteristic
206	C₂	C₂×#90990	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#6653
commutator	C₃×C₅×C₈	C₂²×C₄
Frattini	C₂×C₈	C₂×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle, prime radical	C₂³×C₃×C₅	D₈
cosocle	C₂×C₃×C₅×C₈	C₂³
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#367
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #11745944	C₂	direct (N × H)
11. C₂×C₅×C₃⋊C₁₆	C₄	semidirect
31. C₅×C₃⋊C₁₆	C₂×C₄	semidirect
65. C₂×C₃⋊C₁₆	Dic₅	semidirect
103. C₃⋊C₁₆	C₂×Dic₅	semidirect
125. C₂×C₃×C₅	#367	semidirect
162. C₃×C₅	C₂×#367	semidirect
172. C₂×C₅	#4490	semidirect
188. C₂×C₃	#64725	semidirect
192. C₅	C₂×#4490	semidirect
202. C₃	C₂×#64725	semidirect
203. C₂	#11745944	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×#91102	2
C₂²×C₅×C₃⋊C₁₆	2
C₂×C₃×#3950	2
#11745944	2
C₂×#64725	3
C₂×#4490	5

Subgroups — C2×#11745944 #14314581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745944 #14314581