Subgroups — C₂×#11746911 #14437938

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91763	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4016	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90968	C₂	1	4	yes	maximal, complemented
5	#11746911	C₂	1	8	yes	maximal, direct product factor
6	C₂×#65002	—	3	1	no	maximal, Hall
7	C₂²×D₆₀	—	2	2	no	—
8	C₂²×D₆₀	C₂²	1	2	yes	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	#91763	—	2	2	no	—
11	#91763	C₂²	1	4	yes	—
12	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
14	C₂×C₃×#683	—	2	2	no	—
15	C₃×#4016	—	2	2	no	—
16	C₃×#4016	C₂²	1	4	yes	complemented
17	C₅×#803	C₂²	1	4	yes	complemented
18	#90968	C₂²	1	16	yes	complemented
19	C₂×#5067	—	5	1	no	maximal, Hall
20	C₂×#4020	—	3	1	no	—
21	C₂×#4016	D₃	1	1	yes	characteristic, complemented
22	C₂×C₅×#97	—	3	1	no	—
23	C₂×#3953	—	3	4	no	—
24	#65002	—	3	8	no	—
25	C₂³×D₁₅	—	2	2	no	—
26	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
27	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
28	C₂×D₆₀	—	2	8	no	—
29	C₂×D₆₀	—	2	2	no	—
30	C₂×D₆₀	—	2	8	no	—
31	C₂×D₆₀	—	4	8	no	—
32	C₂×D₆₀	C₂³	1	4	yes	—
33	C₂²×C₃×Dic₅	—	2	2	no	—
34	C₃×C₄²×C₅	D₄	1	2	yes	—
35	C₃×C₄²×C₅	C₂³	1	2	yes	—
36	C₂×C₅×C₃⋊C₈	—	2	4	no	—
37	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
38	C₃×C₄⋊Dic₅	—	2	2	no	—
39	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
40	C₃×#683	—	2	8	no	—
41	C₂×C₃×#125	—	5	1	no	—
42	C₂×#874	—	5	1	no	—
43	#5067	—	5	8	no	—
44	C₂×#809	—	5	4	no	—
45	C₂×#803	D₅	1	1	yes	characteristic, complemented
46	C₂²×D₂₀	—	3	2	no	—
47	C₂²×D₂₀	—	6	2	no	—
48	C₂²×C₅×C₈	—	3	2	no	—
49	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
50	C₂×C₄⋊Dic₅	C₂×D₃	1	2	yes	—
51	C₂×#683	—	2	2	no	—
52	#4020	—	3	4	no	—
53	#4020	—	6	2	no	—
54	#4016	—	2	2	no	—
55	#4016	C₂×D₃	1	4	yes	complemented
56	C₅×#97	—	3	4	no	—
57	#3953	—	3	16	no	—
58	C₂×#490	—	15	1	no	Sylow
59	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
60	C₂²×D₁₅	—	2	4	no	—
61	C₂²×D₁₅	—	4	4	no	—
62	C₂²×D₁₅	—	4	8	no	—
63	C₂×C₃×C₄×C₅	—	2	4	no	—
64	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
65	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
66	C₂×C₃×C₄×C₅	#41	1	4	yes	—
67	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
68	D₆₀	—	2	8	no	—
69	D₆₀	—	4	16	no	—
70	D₆₀	—	4	4	no	—
71	C₂×C₃×Dic₅	—	2	4	no	—
72	C₂×C₃×Dic₅	—	4	4	no	—
73	C₅×C₃⋊C₈	—	2	4	no	—
74	C₂²×D₁₂	—	5	2	no	—
75	C₂²×D₁₂	—	10	2	no	—
76	C₃×#125	—	5	4	no	—
77	C₃×#125	—	10	2	no	—
78	C₂×C₃×C₄⋊C₄	—	5	2	no	—
79	C₂×C₃×C₄⋊C₄	—	10	2	no	—
80	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
81	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
82	#874	—	5	4	no	—
83	#874	—	10	2	no	—
84	#809	—	5	16	no	—
85	#803	C₂×D₅	1	4	yes	complemented
86	C₂³×D₅	—	6	2	no	—
87	C₂²×C₄×C₅	#67	1	2	yes	—
88	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
89	C₂²×Dic₅	—	2	2	no	—
90	C₂×D₂₀	—	3	4	no	—
91	C₂×D₂₀	—	6	8	no	—
92	C₂×D₂₀	—	6	2	no	—
93	C₂×D₂₀	—	6	8	no	—
94	C₂×D₂₀	—	12	8	no	—
95	C₂×C₅×C₈	—	3	4	no	—
96	C₂×C₅×C₈	—	6	4	no	—
97	C₄²×C₅	#67	1	2	yes	—
98	C₄²×C₅	C₂²×D₃	1	2	yes	—
99	C₄⋊Dic₅	—	2	2	no	—
100	C₄⋊Dic₅	C₂²×D₃	1	4	yes	—
101	#683	—	2	8	no	—
102	C₂×#127	—	15	1	no	—
103	C₂×#125	—	5	1	no	—
104	#490	—	15	8	no	—
105	C₂×#102	—	15	4	no	—
106	C₂×#97	—	3	1	no	—
107	C₂²×C₃×C₅	#124	1	2	yes	—
108	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
109	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
110	C₂×D₁₅	—	4	4	no	—
111	C₂×D₁₅	—	4	8	no	—
112	C₂×D₁₅	—	8	8	no	—
113	C₃×C₄×C₅	—	2	4	no	—
114	C₃×C₄×C₅	#124	1	2	yes	—
115	C₃×C₄×C₅	C₂×#41	1	2	yes	—
116	C₃×Dic₅	—	4	4	no	—
117	C₂³×D₃	—	10	2	no	—
118	C₂²×C₃×C₄	—	10	2	no	—
119	C₂²×C₃×C₄	D₂₀	1	2	yes	—
120	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
121	C₂×D₁₂	—	5	4	no	—
122	C₂×D₁₂	—	10	8	no	—
123	C₂×D₁₂	—	10	8	no	—
124	C₂×D₁₂	—	10	2	no	—
125	C₂×D₁₂	—	20	8	no	—
126	C₃×C₄⋊C₄	—	5	4	no	—
127	C₃×C₄⋊C₄	—	10	8	no	—
128	C₃×C₄⋊C₄	—	10	2	no	—
129	C₃×C₄²	D₂₀	1	2	yes	—
130	C₃×C₄²	C₂²×D₅	1	2	yes	—
131	C₂×C₃⋊C₈	—	2	4	no	—
132	C₂×C₃⋊C₈	C₂²×D₅	1	4	yes	—
133	C₂³×C₅	C₂×#67	1	1	yes	characteristic
134	C₂²×D₅	—	6	4	no	—
135	C₂²×D₅	—	12	4	no	—
136	C₂²×D₅	—	12	8	no	—
137	C₂×C₄×C₅	—	2	4	no	—
138	C₂×C₄×C₅	#239	1	4	yes	—
139	C₂×C₄×C₅	C₂×#67	1	4	yes	—
140	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
141	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
142	C₂×Dic₅	—	2	4	no	—
143	C₂×Dic₅	—	4	4	no	—
144	D₂₀	—	6	8	no	—
145	D₂₀	—	12	16	no	—
146	D₂₀	—	12	4	no	—
147	C₅×C₈	—	6	4	no	—
148	C₂²×D₄	—	15	2	no	—
149	C₂²×D₄	—	30	2	no	—
150	C₂²×C₈	—	3	2	no	—
151	#127	—	15	4	no	—
152	#127	—	30	2	no	—
153	#125	—	5	4	no	—
154	#125	—	10	2	no	—
155	C₂×C₄⋊C₄	—	5	2	no	—
156	C₂×C₄⋊C₄	—	10	2	no	—
157	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
158	#102	—	15	16	no	—
159	#97	—	3	4	no	—
160	C₂×C₃×C₅	#490	1	4	yes	complemented
161	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
162	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
163	D₁₅	—	8	4	no	—
164	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
165	C₂²×D₃	—	10	4	no	—
166	C₂²×D₃	—	20	4	no	—
167	C₂²×D₃	—	20	8	no	—
168	C₂×C₃×C₄	—	2	4	no	—
169	C₂×C₃×C₄	—	10	4	no	—
170	C₂×C₃×C₄	—	20	4	no	—
171	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
172	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
173	C₂×C₃×C₄	#709	1	4	yes	—
174	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
175	D₁₂	—	10	8	no	—
176	D₁₂	—	20	16	no	—
177	D₁₂	—	20	4	no	—
178	C₃⋊C₈	—	2	4	no	—
179	C₂²×C₅	#947	1	2	yes	—
180	C₂²×C₅	#949	1	4	yes	—
181	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
182	C₂×D₅	—	12	4	no	—
183	C₂×D₅	—	12	8	no	—
184	C₂×D₅	—	24	8	no	—
185	C₄×C₅	—	2	4	no	—
186	C₄×C₅	#947	1	2	yes	—
187	C₄×C₅	C₂×#239	1	2	yes	—
188	Dic₅	—	4	4	no	—
189	C₂⁴	—	30	2	no	—
190	C₂×D₄	—	15	4	no	—
191	C₂×D₄	—	30	8	no	—
192	C₂×D₄	—	30	8	no	—
193	C₂×D₄	—	30	2	no	—
194	C₂×D₄	—	60	8	no	—
195	C₂²×C₄	—	10	2	no	—
196	C₂²×C₄	#1202	1	2	yes	—
197	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
198	C₂×C₈	—	3	4	no	—
199	C₂×C₈	—	6	4	no	—
200	C₄⋊C₄	—	5	4	no	—
201	C₄⋊C₄	—	10	2	no	—
202	C₄⋊C₄	—	10	8	no	—
203	C₄²	#1202	1	2	yes	—
204	C₄²	C₂×D₃×D₅	1	2	yes	—
205	C₃×C₅	C₂×#490	1	1	yes	characteristic, complemented, Hall
206	C₂²×C₃	#4021	1	2	yes	—
207	C₂²×C₃	#4054	1	4	yes	—
208	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
209	C₂×D₃	—	20	4	no	—
210	C₂×D₃	—	20	8	no	—
211	C₂×D₃	—	40	8	no	—
212	C₃×C₄	—	2	4	no	—
213	C₃×C₄	—	20	4	no	—
214	C₃×C₄	#4021	1	2	yes	—
215	C₃×C₄	C₂×#709	1	2	yes	—
216	C₂×C₅	#5067	1	4	yes	complemented
217	C₂×C₅	C₂×#947	1	1	yes	characteristic
218	C₂×C₅	C₂×#949	1	2	yes	—
219	D₅	—	24	4	no	—
220	C₂³	—	30	4	no	—
221	C₂³	—	60	8	no	—
222	C₂³	—	60	4	no	—
223	C₂³	C₂×#1202	1	1	yes	characteristic
224	D₄	—	30	8	no	—
225	D₄	—	60	16	no	—
226	D₄	—	60	4	no	—
227	C₂×C₄	—	2	4	no	—
228	C₂×C₄	—	10	4	no	—
229	C₂×C₄	—	20	4	no	—
230	C₂×C₄	#6769	1	4	yes	—
231	C₂×C₄	C₂×#1202	1	4	yes	—
232	C₂×C₄	C₂×#1202	1	1	yes	characteristic
233	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
234	C₈	—	6	4	no	—
235	C₂×C₃	#65002	1	4	yes	complemented
236	C₂×C₃	C₂×#4021	1	1	yes	characteristic
237	C₂×C₃	C₂×#4054	1	2	yes	—
238	D₃	—	40	4	no	—
239	C₅	C₂×#5067	1	1	yes	characteristic, complemented, Sylow
240	C₂²	—	60	4	no	—
241	C₂²	—	60	8	no	—
242	C₂²	—	120	8	no	—
243	C₂²	#91301	1	4	yes	—
244	C₂²	#91374	1	2	yes	—
245	C₂²	C₂²×#1202	1	1	yes	characteristic
246	C₄	—	2	4	no	—
247	C₄	—	20	4	no	—
248	C₄	#91374	1	2	yes	—
249	C₄	C₂×#6769	1	2	yes	—
250	C₃	C₂×#65002	1	1	yes	characteristic, complemented, Sylow
251	C₂	—	120	4	no	—
252	C₂	#11746911	1	4	yes	direct product factor
253	C₂	C₂×#91301	1	2	yes	—
254	C₂	C₂×#91374	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1202
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×#91763	C₂
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₂×#490
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4016	C₂	semidirect
3. C₂×C₅×#803	C₂	semidirect
4. C₂×#90968	C₂	semidirect
5. #11746911	C₂	direct (N × H)
16. C₃×#4016	C₂²	semidirect
17. C₅×#803	C₂²	semidirect
18. #90968	C₂²	semidirect
21. C₂×#4016	D₃	semidirect
45. C₂×#803	D₅	semidirect
55. #4016	C₂×D₃	semidirect
85. #803	C₂×D₅	semidirect
160. C₂×C₃×C₅	#490	semidirect
205. C₃×C₅	C₂×#490	semidirect
216. C₂×C₅	#5067	semidirect
235. C₂×C₃	#65002	semidirect
239. C₅	C₂×#5067	semidirect
250. C₃	C₂×#65002	semidirect
252. C₂	#11746911	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×#91763	2
C₂×C₃×#4016	2
C₂×C₅×#803	2
C₂×#90968	2
#11746911	2
C₂×#65002	3
C₂×#5067	5

Subgroups — C2×#11746911 #14437938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11746911 #14437938