Subgroups — C₂×#11750804 #14437958

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91759	C₂	1	1	yes	maximal, characteristic
2	C₂×#91758	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×#91100	C₂	1	4	yes	maximal
5	#11750804	C₂	1	8	yes	maximal, direct product factor
6	C₂×#64992	—	3	1	no	maximal, Hall
7	C₂²×Dic₃₀	C₂²	1	2	yes	—
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₅	—	2	2	no	—
11	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
12	C₂×#6712	—	2	2	no	—
13	#91759	—	2	2	no	—
14	#91759	C₂²	1	4	yes	—
15	#91758	—	2	2	no	—
16	#91758	C₂²	1	4	yes	—
17	C₃×C₅×#97	C₂²	1	4	yes	—
18	#91100	C₂²	1	16	yes	—
19	C₂×#4703	—	5	1	no	maximal, Hall
20	C₂×#4016	—	3	1	no	—
21	C₂×#4015	—	3	1	no	—
22	C₂×C₅×#97	D₃	1	1	yes	characteristic
23	C₂×#3948	—	3	4	no	—
24	#64992	—	3	8	no	—
25	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
26	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₅	—	2	2	no	—
28	C₂²×Dic₁₅	—	2	2	no	—
29	C₂×Dic₃₀	—	2	8	no	—
30	C₂×Dic₃₀	—	2	2	no	—
31	C₂×Dic₃₀	C₂³	1	4	yes	—
32	C₂×C₃×C₅×C₈	—	2	4	no	—
33	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
34	C₃×C₄²×C₅	D₄	1	2	yes	—
35	C₃×C₄²×C₅	C₂³	1	2	yes	—
36	C₄⋊Dic₁₅	—	2	8	no	—
37	C₄⋊Dic₁₅	—	2	2	no	—
38	C₄⋊Dic₁₅	C₂³	1	4	yes	—
39	#6712	—	2	8	no	—
40	C₂×#870	—	5	1	no	—
41	C₂×#869	—	5	1	no	—
42	C₂×C₃×#97	D₅	1	1	yes	characteristic
43	C₂×#816	—	5	4	no	—
44	#4703	—	5	8	no	—
45	C₂²×Dic₁₀	—	3	2	no	—
46	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
47	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
48	C₂×C₄⋊Dic₅	—	3	2	no	—
49	C₂×C₄⋊Dic₅	—	6	2	no	—
50	C₂×#683	—	6	2	no	—
51	#4016	—	3	4	no	—
52	#4016	—	6	2	no	—
53	#4015	—	3	4	no	—
54	#4015	—	6	2	no	—
55	C₅×#97	C₂×D₃	1	4	yes	—
56	#3948	—	3	16	no	—
57	C₂×#491	—	15	1	no	Sylow
58	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	—	2	4	no	—
60	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
61	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	#41	1	4	yes	—
63	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
64	C₂×Dic₁₅	—	2	4	no	—
65	C₂×Dic₁₅	—	2	4	no	—
66	C₂×Dic₁₅	—	4	4	no	—
67	C₂×Dic₁₅	—	4	4	no	—
68	Dic₃₀	—	2	8	no	—
69	Dic₃₀	—	4	4	no	—
70	C₃×C₅×C₈	—	2	4	no	—
71	C₂²×Dic₆	—	5	2	no	—
72	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
73	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
74	C₂×C₄⋊Dic₃	—	5	2	no	—
75	C₂×C₄⋊Dic₃	—	10	2	no	—
76	C₂×Dic₃⋊C₄	—	10	2	no	—
77	#870	—	5	4	no	—
78	#870	—	10	2	no	—
79	#869	—	5	4	no	—
80	#869	—	10	2	no	—
81	C₃×#97	C₂×D₅	1	4	yes	—
82	#816	—	5	16	no	—
83	C₂²×C₄×C₅	D₁₂	1	2	yes	—
84	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
85	C₂²×Dic₅	—	6	2	no	—
86	C₂²×Dic₅	—	6	2	no	—
87	C₂×Dic₁₀	—	3	4	no	—
88	C₂×Dic₁₀	—	6	8	no	—
89	C₂×Dic₁₀	—	6	2	no	—
90	C₂×C₅×C₈	—	2	4	no	—
91	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
92	C₄²×C₅	D₁₂	1	2	yes	—
93	C₄²×C₅	C₂²×D₃	1	2	yes	—
94	C₄⋊Dic₅	—	3	4	no	—
95	C₄⋊Dic₅	—	6	8	no	—
96	C₄⋊Dic₅	—	6	2	no	—
97	#683	—	6	8	no	—
98	C₂×C₄⋊Q₈	—	15	1	no	—
99	C₂×#125	—	15	1	no	—
100	#491	—	15	8	no	—
101	C₂×#103	—	15	4	no	—
102	C₂×#97	D₁₅	1	1	yes	characteristic
103	C₂²×C₃×C₅	#124	1	2	yes	—
104	C₂²×C₃×C₅	#137	1	4	yes	—
105	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
106	C₃×C₄×C₅	—	2	4	no	—
107	C₃×C₄×C₅	#124	1	2	yes	—
108	C₃×C₄×C₅	C₂×#41	1	2	yes	—
109	Dic₁₅	—	4	4	no	—
110	Dic₁₅	—	4	4	no	—
111	C₂²×C₃×C₄	D₂₀	1	2	yes	—
112	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
113	C₂²×Dic₃	—	10	2	no	—
114	C₂²×Dic₃	—	10	2	no	—
115	C₂×Dic₆	—	5	4	no	—
116	C₂×Dic₆	—	10	8	no	—
117	C₂×Dic₆	—	10	2	no	—
118	C₂×C₃×C₈	—	2	4	no	—
119	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
120	C₃×C₄²	D₂₀	1	2	yes	—
121	C₃×C₄²	C₂²×D₅	1	2	yes	—
122	C₄⋊Dic₃	—	5	4	no	—
123	C₄⋊Dic₃	—	10	8	no	—
124	C₄⋊Dic₃	—	10	2	no	—
125	Dic₃⋊C₄	—	10	8	no	—
126	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
127	C₂×C₄×C₅	—	2	4	no	—
128	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
129	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
130	C₂×C₄×C₅	#235	1	4	yes	—
131	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
132	C₂×Dic₅	—	6	4	no	—
133	C₂×Dic₅	—	6	4	no	—
134	C₂×Dic₅	—	12	4	no	—
135	C₂×Dic₅	—	12	4	no	—
136	Dic₁₀	—	6	8	no	—
137	Dic₁₀	—	12	4	no	—
138	C₅×C₈	—	2	4	no	—
139	C₂²×Q₈	—	15	2	no	—
140	C₂²×C₈	C₂×D₁₅	1	2	yes	—
141	C₄⋊Q₈	—	15	4	no	—
142	C₄⋊Q₈	—	30	2	no	—
143	#125	—	15	4	no	—
144	#125	—	30	2	no	—
145	C₂×C₄⋊C₄	—	15	2	no	—
146	C₂×C₄⋊C₄	—	30	2	no	—
147	C₂×C₄⋊C₄	—	30	2	no	—
148	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
149	#103	—	15	16	no	—
150	#97	C₂×D₁₅	1	4	yes	—
151	C₂×C₃×C₅	#491	1	4	yes	complemented
152	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
153	C₂×C₃×C₅	C₂×#137	1	2	yes	—
154	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
155	C₂×C₃×C₄	—	2	4	no	—
156	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
157	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
158	C₂×C₃×C₄	#709	1	4	yes	—
159	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
160	C₂×Dic₃	—	10	4	no	—
161	C₂×Dic₃	—	10	4	no	—
162	C₂×Dic₃	—	20	4	no	—
163	C₂×Dic₃	—	20	4	no	—
164	Dic₆	—	10	8	no	—
165	Dic₆	—	20	4	no	—
166	C₃×C₈	—	2	4	no	—
167	C₂²×C₅	#875	1	2	yes	—
168	C₂²×C₅	#909	1	4	yes	—
169	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
170	C₄×C₅	—	2	4	no	—
171	C₄×C₅	#875	1	2	yes	—
172	C₄×C₅	C₂×#235	1	2	yes	—
173	Dic₅	—	12	4	no	—
174	Dic₅	—	12	4	no	—
175	C₂×Q₈	—	15	4	no	—
176	C₂×Q₈	—	30	2	no	—
177	C₂×Q₈	—	30	8	no	—
178	C₂²×C₄	—	30	2	no	—
179	C₂²×C₄	—	30	2	no	—
180	C₂²×C₄	D₆₀	1	2	yes	—
181	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	C₂²×D₁₅	1	4	yes	—
184	C₄⋊C₄	—	15	4	no	—
185	C₄⋊C₄	—	30	2	no	—
186	C₄⋊C₄	—	30	8	no	—
187	C₄⋊C₄	—	30	8	no	—
188	C₄²	D₆₀	1	2	yes	—
189	C₄²	C₂²×D₁₅	1	2	yes	—
190	C₃×C₅	C₂×#491	1	1	yes	characteristic, complemented, Hall
191	C₂²×C₃	#4021	1	2	yes	—
192	C₂²×C₃	#4055	1	4	yes	—
193	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
194	C₃×C₄	—	2	4	no	—
195	C₃×C₄	#4021	1	2	yes	—
196	C₃×C₄	C₂×#709	1	2	yes	—
197	Dic₃	—	20	4	no	—
198	Dic₃	—	20	4	no	—
199	C₂×C₅	#4703	1	4	yes	complemented
200	C₂×C₅	C₂×#875	1	1	yes	characteristic
201	C₂×C₅	C₂×#909	1	2	yes	—
202	C₂³	C₂×D₆₀	1	1	yes	characteristic
203	Q₈	—	30	8	no	—
204	Q₈	—	60	4	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	30	4	no	—
207	C₂×C₄	—	30	4	no	—
208	C₂×C₄	—	60	4	no	—
209	C₂×C₄	—	60	4	no	—
210	C₂×C₄	C₂×D₆₀	1	4	yes	—
211	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
212	C₂×C₄	#6817	1	4	yes	—
213	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
214	C₈	—	2	4	no	—
215	C₂×C₃	#64992	1	4	yes	complemented
216	C₂×C₃	C₂×#4021	1	1	yes	characteristic
217	C₂×C₃	C₂×#4055	1	2	yes	—
218	C₅	C₂×#4703	1	1	yes	characteristic, complemented, Sylow
219	C₂²	#91764	1	2	yes	—
220	C₂²	#91798	1	4	yes	—
221	C₂²	C₂²×D₆₀	1	1	yes	characteristic
222	C₄	—	2	4	no	—
223	C₄	—	60	4	no	—
224	C₄	—	60	4	no	—
225	C₄	#91764	1	2	yes	—
226	C₄	C₂×#6817	1	2	yes	—
227	C₃	C₂×#64992	1	1	yes	characteristic, complemented, Sylow
228	C₂	#11750804	1	4	yes	direct product factor
229	C₂	C₂×#91764	1	1	yes	characteristic
230	C₂	C₂×#91798	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₆₀
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×#97	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×#97	D₁₅
hypocenter	C₃×C₅	C₂×#491
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
5. #11750804	C₂	direct (N × H)
151. C₂×C₃×C₅	#491	semidirect
190. C₃×C₅	C₂×#491	semidirect
199. C₂×C₅	#4703	semidirect
215. C₂×C₃	#64992	semidirect
218. C₅	C₂×#4703	semidirect
227. C₃	C₂×#64992	semidirect
228. C₂	#11750804	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×#91759	2
C₂×#91758	2
C₂×C₃×C₅×#97	2
C₂×#91100	2
#11750804	2
C₂×#64992	3
C₂×#4703	5

Subgroups — C2×#11750804 #14437958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11750804 #14437958