Subgroups — C₂×C₃×#64966 #14332001

Order 1920.

1816 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#685	C₂	1	3	yes	maximal
2	C₂²×C₃×C₄⋊Dic₅	C₂	1	3	yes	maximal, complemented
3	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64966	C₂	1	8	yes	maximal, direct product factor
5	C₂×#64966	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
7	C₂³×C₃×C₄×C₅	C₂²	1	3	yes	—
8	C₂³×C₃×Dic₅	C₂²	1	3	yes	—
9	C₂×C₃×#685	—	2	12	no	—
10	C₂×C₃×#685	C₂²	1	12	yes	—
11	C₂×C₃×C₄⋊Dic₅	—	2	12	no	—
12	C₂×C₃×C₄⋊Dic₅	C₂²	1	12	yes	complemented
13	C₃×C₅×#95	C₂²	1	4	yes	complemented
14	C₂×C₃×#399	—	5	1	no	maximal, Hall
15	C₂²×#685	C₂×C₃	1	3	yes	—
16	C₂²×C₄⋊Dic₅	C₂×C₃	1	3	yes	complemented
17	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic, complemented
18	#64966	C₂×C₃	1	8	yes	direct product factor
19	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
20	C₂³×C₃×D₅	—	2	6	no	—
21	C₂³×C₃×D₅	—	2	6	no	—
22	C₂³×C₃×D₅	Q₈	1	4	yes	—
23	C₂³×C₃×D₅	C₂³	1	2	yes	—
24	C₂²×C₃×C₄×C₅	—	2	12	no	—
25	C₂²×C₃×C₄×C₅	D₄	1	12	yes	—
26	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
27	C₂²×C₃×Dic₅	—	2	12	no	—
28	C₂²×C₃×Dic₅	—	2	6	no	—
29	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
30	C₃×#685	—	2	24	no	—
31	C₃×C₄⋊Dic₅	—	2	24	no	—
32	C₂²×C₃×C₄⋊C₄	—	5	3	no	—
33	C₂²×C₃×C₂²⋊C₄	—	5	3	no	—
34	C₃×#399	—	5	8	no	—
35	C₂×C₃×#95	D₅	1	1	yes	characteristic, complemented
36	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
37	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	—
38	C₂³×Dic₅	C₂²×C₃	1	3	yes	—
39	C₂×#685	—	2	12	no	—
40	C₂×#685	C₂²×C₃	1	12	yes	—
41	C₂×C₄⋊Dic₅	—	2	12	no	—
42	C₂×C₄⋊Dic₅	C₂²×C₃	1	12	yes	complemented
43	C₅×#95	C₂²×C₃	1	4	yes	complemented
44	C₂×#399	—	5	1	no	Sylow
45	C₂³×C₃×C₅	C₂×D₄	1	6	yes	—
46	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
47	C₂³×C₃×C₅	#41	1	6	yes	—
48	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
49	C₂²×C₃×D₅	—	2	24	no	—
50	C₂²×C₃×D₅	—	2	6	no	—
51	C₂²×C₃×D₅	—	2	6	no	—
52	C₂²×C₃×D₅	—	4	12	no	—
53	C₂²×C₃×D₅	—	4	4	no	—
54	C₂²×C₃×D₅	C₂×Q₈	1	4	yes	—
55	C₂×C₃×C₄×C₅	—	2	24	no	—
56	C₂×C₃×C₄×C₅	—	2	12	no	—
57	C₂×C₃×C₄×C₅	C₂×D₄	1	12	yes	—
58	C₂×C₃×Dic₅	—	2	12	no	—
59	C₂×C₃×Dic₅	—	2	6	no	—
60	C₂×C₃×Dic₅	—	4	12	no	—
61	C₂⁵×C₃	—	5	1	no	—
62	C₂³×C₃×C₄	—	5	3	no	—
63	C₂³×C₃×C₄	C₂×D₅	1	3	yes	—
64	C₂×C₃×C₄⋊C₄	—	5	12	no	—
65	C₂×C₃×C₄⋊C₄	—	10	12	no	—
66	C₂×C₃×C₂²⋊C₄	—	5	12	no	—
67	C₂×C₃×C₂²⋊C₄	—	10	12	no	—
68	C₃×#95	C₂×D₅	1	4	yes	complemented
69	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
70	C₂³×D₅	—	2	6	no	—
71	C₂³×D₅	—	2	6	no	—
72	C₂³×D₅	C₃×Q₈	1	4	yes	—
73	C₂³×D₅	C₂³×C₃	1	2	yes	—
74	C₂²×C₄×C₅	—	2	12	no	—
75	C₂²×C₄×C₅	C₃×D₄	1	12	yes	—
76	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
77	C₂²×Dic₅	—	2	12	no	—
78	C₂²×Dic₅	—	2	6	no	—
79	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
80	#685	—	2	24	no	—
81	C₄⋊Dic₅	—	2	24	no	—
82	C₂²×C₄⋊C₄	—	5	3	no	—
83	C₂²×C₂²⋊C₄	—	5	3	no	—
84	#399	—	5	8	no	—
85	C₂×#95	C₃×D₅	1	1	yes	characteristic, complemented
86	C₂²×C₃×C₅	C₂²⋊Q₈	1	12	yes	—
87	C₂²×C₃×C₅	#123	1	12	yes	—
88	C₂²×C₃×C₅	#127	1	4	yes	—
89	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
90	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
91	C₂²×C₃×C₅	C₂×#41	1	3	yes	—
92	C₂×C₃×D₅	—	2	12	no	—
93	C₂×C₃×D₅	—	4	6	no	—
94	C₂×C₃×D₅	—	4	2	no	—
95	C₂×C₃×D₅	—	4	16	no	—
96	C₃×C₄×C₅	—	2	12	no	—
97	C₃×Dic₅	—	4	6	no	—
98	C₂⁴×C₃	—	5	4	no	—
99	C₂⁴×C₃	—	5	2	no	—
100	C₂⁴×C₃	—	10	6	no	—
101	C₂⁴×C₃	—	10	6	no	—
102	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
103	C₂²×C₃×C₄	—	2	12	no	—
104	C₂²×C₃×C₄	—	5	6	no	—
105	C₂²×C₃×C₄	—	10	6	no	—
106	C₂²×C₃×C₄	—	10	12	no	—
107	C₂²×C₃×C₄	D₂₀	1	12	yes	—
108	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
109	C₃×C₄⋊C₄	—	10	24	no	—
110	C₃×C₂²⋊C₄	—	10	24	no	—
111	C₂³×C₅	C₂×C₃×D₄	1	6	yes	—
112	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
113	C₂³×C₅	C₃×#41	1	6	yes	—
114	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
115	C₂²×D₅	—	2	24	no	—
116	C₂²×D₅	—	2	6	no	—
117	C₂²×D₅	—	2	6	no	—
118	C₂²×D₅	—	4	12	no	—
119	C₂²×D₅	—	4	4	no	—
120	C₂²×D₅	C₂×C₃×Q₈	1	4	yes	—
121	C₂×C₄×C₅	—	2	24	no	—
122	C₂×C₄×C₅	—	2	12	no	—
123	C₂×C₄×C₅	C₂×C₃×D₄	1	12	yes	—
124	C₂×Dic₅	—	2	12	no	—
125	C₂×Dic₅	—	2	6	no	—
126	C₂×Dic₅	—	4	12	no	—
127	C₂⁵	—	5	1	no	—
128	C₂³×C₄	—	5	3	no	—
129	C₂³×C₄	C₂×C₃×D₅	1	3	yes	—
130	C₂×C₄⋊C₄	—	5	12	no	—
131	C₂×C₄⋊C₄	—	10	12	no	—
132	C₂×C₂²⋊C₄	—	5	12	no	—
133	C₂×C₂²⋊C₄	—	10	12	no	—
134	#95	C₂×C₃×D₅	1	4	yes	complemented
135	C₂×C₃×C₅	#399	1	8	yes	complemented
136	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	3	yes	—
137	C₂×C₃×C₅	C₂×#123	1	3	yes	—
138	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
139	C₃×D₅	—	4	4	no	—
140	C₂³×C₃	—	5	4	no	—
141	C₂³×C₃	—	10	6	no	—
142	C₂³×C₃	—	10	6	no	—
143	C₂³×C₃	—	10	24	no	—
144	C₂³×C₃	—	20	4	no	—
145	C₂³×C₃	—	20	12	no	—
146	C₂³×C₃	C₂×D₂₀	1	6	yes	—
147	C₂³×C₃	#711	1	6	yes	—
148	C₂³×C₃	Q₈×D₅	1	2	yes	—
149	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
150	C₂×C₃×C₄	—	2	12	no	—
151	C₂×C₃×C₄	—	2	24	no	—
152	C₂×C₃×C₄	—	10	6	no	—
153	C₂×C₃×C₄	—	10	12	no	—
154	C₂×C₃×C₄	—	20	12	no	—
155	C₂×C₃×C₄	C₂×D₂₀	1	12	yes	—
156	C₂²×C₅	C₃×C₂²⋊Q₈	1	12	yes	—
157	C₂²×C₅	C₃×#123	1	12	yes	—
158	C₂²×C₅	C₃×#127	1	4	yes	—
159	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
160	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
161	C₂²×C₅	C₂×C₃×#41	1	3	yes	—
162	C₂×D₅	—	2	12	no	—
163	C₂×D₅	—	4	16	no	—
164	C₂×D₅	—	4	6	no	—
165	C₂×D₅	—	4	2	no	—
166	C₄×C₅	—	2	12	no	—
167	Dic₅	—	4	6	no	—
168	C₂⁴	—	5	4	no	—
169	C₂⁴	—	5	2	no	—
170	C₂⁴	—	10	6	no	—
171	C₂⁴	—	10	6	no	—
172	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
173	C₂²×C₄	—	2	12	no	—
174	C₂²×C₄	—	5	6	no	—
175	C₂²×C₄	—	10	6	no	—
176	C₂²×C₄	—	10	12	no	—
177	C₂²×C₄	C₃×D₂₀	1	12	yes	—
178	C₂²×C₄	C₂²×C₃×D₅	1	6	yes	—
179	C₄⋊C₄	—	10	24	no	—
180	C₂²⋊C₄	—	10	24	no	—
181	C₃×C₅	C₂×#399	1	1	yes	characteristic, complemented, Hall
182	C₂²×C₃	—	10	12	no	—
183	C₂²×C₃	—	20	2	no	—
184	C₂²×C₃	—	20	6	no	—
185	C₂²×C₃	—	20	16	no	—
186	C₂²×C₃	#4020	1	4	yes	—
187	C₂²×C₃	#4032	1	12	yes	—
188	C₂²×C₃	#4043	1	12	yes	—
189	C₂²×C₃	C₂²×D₂₀	1	3	yes	—
190	C₂²×C₃	C₂×#711	1	3	yes	—
191	C₂²×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
192	C₃×C₄	—	2	12	no	—
193	C₃×C₄	—	20	6	no	—
194	C₂×C₅	C₃×#399	1	8	yes	complemented
195	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	3	yes	—
196	C₂×C₅	C₂×C₃×#123	1	3	yes	—
197	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
198	D₅	—	4	4	no	—
199	C₂³	—	5	4	no	—
200	C₂³	—	10	6	no	—
201	C₂³	—	10	6	no	—
202	C₂³	—	10	24	no	—
203	C₂³	—	20	4	no	—
204	C₂³	—	20	12	no	—
205	C₂³	C₂×C₃×D₂₀	1	6	yes	—
206	C₂³	C₃×#711	1	6	yes	—
207	C₂³	C₃×Q₈×D₅	1	2	yes	—
208	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
209	C₂×C₄	—	2	12	no	—
210	C₂×C₄	—	2	24	no	—
211	C₂×C₄	—	10	6	no	—
212	C₂×C₄	—	10	12	no	—
213	C₂×C₄	—	20	12	no	—
214	C₂×C₄	C₂×C₃×D₂₀	1	12	yes	—
215	C₂×C₃	—	20	4	no	—
216	C₂×C₃	#64966	1	8	yes	direct product factor
217	C₂×C₃	C₂×#4020	1	1	yes	characteristic
218	C₂×C₃	C₂×#4032	1	3	yes	—
219	C₂×C₃	C₂×#4043	1	3	yes	—
220	C₅	C₂×C₃×#399	1	1	yes	characteristic, complemented, Sylow
221	C₂²	—	10	12	no	—
222	C₂²	—	20	16	no	—
223	C₂²	—	20	2	no	—
224	C₂²	—	20	6	no	—
225	C₂²	C₃×#4020	1	4	yes	—
226	C₂²	C₃×#4032	1	12	yes	—
227	C₂²	C₃×#4043	1	12	yes	—
228	C₂²	C₂²×C₃×D₂₀	1	3	yes	—
229	C₂²	C₂×C₃×#711	1	3	yes	—
230	C₂²	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
231	C₄	—	2	12	no	—
232	C₄	—	20	6	no	—
233	C₃	C₂×#64966	1	1	yes	characteristic, direct product factor, Sylow
234	C₂	—	20	4	no	—
235	C₂	C₃×#64966	1	8	yes	direct product factor
236	C₂	C₂×C₃×#4020	1	1	yes	characteristic
237	C₂	C₂×C₃×#4032	1	3	yes	—
238	C₂	C₂×C₃×#4043	1	3	yes	—

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₅
commutator, cosocle	C₂³×C₅	C₂⁴×C₃
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#95	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂⁴×C₃×D₅	C₂²
hypercenter	C₂×C₃×#95	D₅
hypocenter	C₅	C₂×C₃×#399
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂×C₃×#95

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄⋊Dic₅	C₂	semidirect
3. C₂×C₃×C₅×#95	C₂	semidirect
4. C₃×#64966	C₂	direct (N × H)
5. C₂×#64966	C₃	direct (N × H)
12. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
13. C₃×C₅×#95	C₂²	semidirect
16. C₂²×C₄⋊Dic₅	C₂×C₃	semidirect
17. C₂×C₅×#95	C₂×C₃	semidirect
18. #64966	C₂×C₃	direct (N × H)
35. C₂×C₃×#95	D₅	semidirect
42. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
43. C₅×#95	C₂²×C₃	semidirect
68. C₃×#95	C₂×D₅	semidirect
85. C₂×#95	C₃×D₅	semidirect
134. #95	C₂×C₃×D₅	semidirect
135. C₂×C₃×C₅	#399	semidirect
181. C₃×C₅	C₂×#399	semidirect
194. C₂×C₅	C₃×#399	semidirect
216. C₂×C₃	#64966	direct (N × H)
220. C₅	C₂×C₃×#399	semidirect
233. C₃	C₂×#64966	direct (N × H)
235. C₂	C₃×#64966	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×#685	2
C₂²×C₃×C₄⋊Dic₅	2
C₂×C₃×C₅×#95	2
C₃×#64966	2
C₂×#64966	3
C₂×C₃×#399	5

Subgroups — C2×C3×#64966 #14332001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64966 #14332001