Subgroups — C₂×C₅×#3963 #13102469

Order 1600.

896 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	C₂³×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×Dic₅	C₂	1	2	yes	maximal
3	C₅×#3963	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₅²	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₅²	—	2	4	no	—
6	C₂²×C₄×C₅²	C₄	1	4	yes	complemented
7	C₂²×C₄×C₅²	C₂²	1	2	yes	—
8	C₂²×C₅×Dic₅	—	2	4	no	—
9	C₂²×C₅×Dic₅	—	2	4	no	—
10	C₂²×C₅×Dic₅	C₄	1	8	yes	complemented
11	C₂²×C₅×Dic₅	C₂²	1	4	yes	—
12	C₂×C₅×#95	—	5	1	no	maximal
13	C₂×#3963	C₅	1	1	yes	maximal, characteristic, direct product factor
14	C₂³×C₅²	C₂×C₄	1	4	yes	—
15	C₂³×C₅²	C₂×C₄	1	2	yes	—
16	C₂³×C₅²	D₄	1	2	yes	—
17	C₂³×C₅²	D₄	1	4	yes	—
18	C₂³×C₅²	Q₈	1	2	yes	—
19	C₂³×C₅²	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₅²	—	2	8	no	—
21	C₂×C₄×C₅²	—	2	4	no	—
22	C₂×C₄×C₅²	C₂×C₄	1	4	yes	complemented
23	C₂×C₅×Dic₅	—	2	16	no	—
24	C₂×C₅×Dic₅	—	2	4	no	—
25	C₂×C₅×Dic₅	—	2	4	no	—
26	C₂×C₅×Dic₅	C₂×C₄	1	8	yes	complemented
27	C₂³×C₄×C₅	—	2	2	no	—
28	C₂³×C₄×C₅	—	5	2	no	—
29	C₂³×C₄×C₅	D₅	1	1	yes	characteristic
30	C₂³×C₄×C₅	C₂×C₅	1	1	yes	characteristic
31	C₂³×Dic₅	C₂×C₅	1	2	yes	—
32	C₅×#95	—	5	4	no	—
33	#3963	C₂×C₅	1	4	yes	direct product factor
34	C₂²×C₅²	C₄²	1	4	yes	—
35	C₂²×C₅²	C₂²⋊C₄	1	8	yes	—
36	C₂²×C₅²	C₂²⋊C₄	1	4	yes	—
37	C₂²×C₅²	C₄⋊C₄	1	8	yes	—
38	C₂²×C₅²	C₄⋊C₄	1	4	yes	—
39	C₂²×C₅²	C₂²×C₄	1	2	yes	—
40	C₂²×C₅²	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₅²	C₂×D₄	1	2	yes	—
43	C₂²×C₅²	C₂×Q₈	1	1	yes	characteristic
44	C₄×C₅²	—	2	4	no	—
45	C₅×Dic₅	—	2	8	no	—
46	C₂⁴×C₅	—	2	2	no	—
47	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic
48	C₂⁴×C₅	C₂²×C₅	1	1	yes	characteristic
49	C₂²×C₄×C₅	—	2	16	no	—
50	C₂²×C₄×C₅	—	2	4	no	—
51	C₂²×C₄×C₅	—	2	4	no	—
52	C₂²×C₄×C₅	—	2	8	no	—
53	C₂²×C₄×C₅	—	2	4	no	—
54	C₂²×C₄×C₅	—	5	8	no	—
55	C₂²×C₄×C₅	—	5	4	no	—
56	C₂²×C₄×C₅	—	10	4	no	—
57	C₂²×C₄×C₅	—	10	4	no	—
58	C₂²×C₄×C₅	Dic₅	1	4	yes	complemented
59	C₂²×C₄×C₅	C₄×C₅	1	4	yes	complemented
60	C₂²×C₄×C₅	C₂×D₅	1	2	yes	—
61	C₂²×C₄×C₅	C₂²×C₅	1	2	yes	—
62	C₂²×Dic₅	—	2	4	no	—
63	C₂²×Dic₅	—	2	4	no	—
64	C₂²×Dic₅	C₄×C₅	1	8	yes	complemented
65	C₂²×Dic₅	C₂²×C₅	1	4	yes	—
66	C₂×#95	—	5	1	no	Sylow
67	C₂×C₅²	#95	1	8	yes	complemented
68	C₂×C₅²	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₅²	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₅²	C₂×C₂²⋊C₄	1	2	yes	—
71	C₂×C₅²	C₂×C₄⋊C₄	1	2	yes	—
72	C₂×C₅²	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂³×C₅	—	2	4	no	—
74	C₂³×C₅	—	2	8	no	—
75	C₂³×C₅	—	2	4	no	—
76	C₂³×C₅	—	2	4	no	—
77	C₂³×C₅	—	2	8	no	—
78	C₂³×C₅	—	2	2	no	—
79	C₂³×C₅	Dic₁₀	1	2	yes	—
80	C₂³×C₅	C₄×D₅	1	4	yes	—
81	C₂³×C₅	D₂₀	1	2	yes	—
82	C₂³×C₅	C₂×Dic₅	1	2	yes	—
83	C₂³×C₅	C₂²⋊D₅	1	4	yes	—
84	C₂³×C₅	C₂×C₄×C₅	1	4	yes	—
85	C₂³×C₅	C₂×C₄×C₅	1	2	yes	—
86	C₂³×C₅	C₅×D₄	1	2	yes	—
87	C₂³×C₅	C₅×D₄	1	4	yes	—
88	C₂³×C₅	C₅×Q₈	1	2	yes	—
89	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
90	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
91	C₂×C₄×C₅	—	2	16	no	—
92	C₂×C₄×C₅	—	2	32	no	—
93	C₂×C₄×C₅	—	2	8	no	—
94	C₂×C₄×C₅	—	2	8	no	—
95	C₂×C₄×C₅	—	2	4	no	—
96	C₂×C₄×C₅	—	2	4	no	—
97	C₂×C₄×C₅	—	2	8	no	—
98	C₂×C₄×C₅	—	5	8	no	—
99	C₂×C₄×C₅	—	10	16	no	—
100	C₂×C₄×C₅	—	10	4	no	—
101	C₂×C₄×C₅	—	10	4	no	—
102	C₂×C₄×C₅	C₂×Dic₅	1	4	yes	complemented
103	C₂×C₄×C₅	C₂×C₄×C₅	1	4	yes	complemented
104	C₂×Dic₅	—	2	16	no	—
105	C₂×Dic₅	—	2	4	no	—
106	C₂×Dic₅	—	2	4	no	—
107	C₂×Dic₅	C₂×C₄×C₅	1	8	yes	complemented
108	C₂³×C₄	—	5	2	no	—
109	C₂³×C₄	C₅×D₅	1	1	yes	characteristic
110	#95	—	5	4	no	—
111	C₅²	C₂×#95	1	1	yes	characteristic, complemented, Sylow
112	C₂²×C₅	—	2	2	no	—
113	C₂²×C₅	—	2	4	no	—
114	C₂²×C₅	—	2	2	no	—
115	C₂²×C₅	—	2	2	no	—
116	C₂²×C₅	—	2	4	no	—
117	C₂²×C₅	—	2	8	no	—
118	C₂²×C₅	—	2	16	no	—
119	C₂²×C₅	—	2	8	no	—
120	C₂²×C₅	—	2	16	no	—
121	C₂²×C₅	—	2	8	no	—
122	C₂²×C₅	C₄×Dic₅	1	4	yes	—
123	C₂²×C₅	#683	1	8	yes	—
124	C₂²×C₅	C₄⋊Dic₅	1	4	yes	—
125	C₂²×C₅	#685	1	8	yes	—
126	C₂²×C₅	C₂²⋊Dic₅	1	4	yes	—
127	C₂²×C₅	C₄²×C₅	1	4	yes	—
128	C₂²×C₅	C₅×C₂²⋊C₄	1	8	yes	—
129	C₂²×C₅	C₅×C₂²⋊C₄	1	4	yes	—
130	C₂²×C₅	C₅×C₄⋊C₄	1	8	yes	—
131	C₂²×C₅	C₅×C₄⋊C₄	1	4	yes	—
132	C₂²×C₅	C₂×Dic₁₀	1	1	yes	characteristic
133	C₂²×C₅	C₂×C₄×D₅	1	2	yes	—
134	C₂²×C₅	C₂×D₂₀	1	1	yes	characteristic
135	C₂²×C₅	C₂²×Dic₅	1	1	yes	characteristic
136	C₂²×C₅	C₂×C₂²⋊D₅	1	2	yes	—
137	C₂²×C₅	C₂²×C₄×C₅	1	2	yes	—
138	C₂²×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
139	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
140	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
141	C₂²×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
142	C₄×C₅	—	2	16	no	—
143	C₄×C₅	—	2	4	no	—
144	C₄×C₅	—	2	4	no	—
145	C₄×C₅	—	10	8	no	—
146	Dic₅	—	2	8	no	—
147	C₂⁴	C₂×C₅×D₅	1	1	yes	characteristic
148	C₂²×C₄	—	2	4	no	—
149	C₂²×C₄	—	5	8	no	—
150	C₂²×C₄	—	5	4	no	—
151	C₂²×C₄	—	10	4	no	—
152	C₂²×C₄	—	10	4	no	—
153	C₂²×C₄	C₅×Dic₅	1	4	yes	complemented
154	C₂²×C₄	C₂×C₅×D₅	1	2	yes	—
155	C₂×C₅	—	2	2	no	—
156	C₂×C₅	—	2	4	no	—
157	C₂×C₅	—	2	2	no	—
158	C₂×C₅	—	2	4	no	—
159	C₂×C₅	—	2	16	no	—
160	C₂×C₅	—	2	2	no	—
161	C₂×C₅	#3963	1	8	yes	direct product factor
162	C₂×C₅	C₅×#95	1	8	yes	complemented
163	C₂×C₅	C₂×C₄×Dic₅	1	1	yes	characteristic
164	C₂×C₅	C₂×#683	1	2	yes	—
165	C₂×C₅	C₂×C₄⋊Dic₅	1	1	yes	characteristic
166	C₂×C₅	C₂×#685	1	2	yes	—
167	C₂×C₅	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
168	C₂×C₅	C₂×C₄²×C₅	1	1	yes	characteristic
169	C₂×C₅	C₂×C₅×C₂²⋊C₄	1	2	yes	—
170	C₂×C₅	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₅	C₂×C₅×C₄⋊C₄	1	2	yes	—
172	C₂×C₅	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
173	C₂³	C₅×Dic₁₀	1	2	yes	—
174	C₂³	C₄×C₅×D₅	1	4	yes	—
175	C₂³	C₅×D₂₀	1	2	yes	—
176	C₂³	C₂×C₅×Dic₅	1	2	yes	—
177	C₂³	C₅×C₂²⋊D₅	1	4	yes	—
178	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	8	no	—
181	C₂×C₄	—	5	8	no	—
182	C₂×C₄	—	10	4	no	—
183	C₂×C₄	—	10	4	no	—
184	C₂×C₄	—	10	16	no	—
185	C₂×C₄	C₂×C₅×Dic₅	1	4	yes	complemented
186	C₅	—	2	2	no	—
187	C₅	C₂×#3963	1	1	yes	characteristic, direct product factor
188	C₅	C₂×C₅×#95	1	1	yes	characteristic, complemented
189	C₂²	C₄×C₅×Dic₅	1	4	yes	—
190	C₂²	C₅×#683	1	8	yes	—
191	C₂²	C₅×C₄⋊Dic₅	1	4	yes	—
192	C₂²	C₅×#685	1	8	yes	—
193	C₂²	C₅×C₂²⋊Dic₅	1	4	yes	—
194	C₂²	C₂×C₅×Dic₁₀	1	1	yes	characteristic
195	C₂²	C₂×C₄×C₅×D₅	1	2	yes	—
196	C₂²	C₂×C₅×D₂₀	1	1	yes	characteristic
197	C₂²	C₂²×C₅×Dic₅	1	1	yes	characteristic
198	C₂²	C₂×C₅×C₂²⋊D₅	1	2	yes	—
199	C₄	—	2	4	no	—
200	C₄	—	10	8	no	—
201	C₂	C₅×#3963	1	8	yes	direct product factor
202	C₂	C₂×C₄×C₅×Dic₅	1	1	yes	characteristic
203	C₂	C₂×C₅×#683	1	2	yes	—
204	C₂	C₂×C₅×C₄⋊Dic₅	1	1	yes	characteristic
205	C₂	C₂×C₅×#685	1	2	yes	—
206	C₂	C₂×C₅×C₂²⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₅	C₂×D₅
commutator	C₂×C₅	C₂×C₄²×C₅
Frattini	C₂³	C₂²×C₅×D₅
Fitting	C₂³×C₄×C₅²	C₂
socle, prime radical	C₂⁴×C₅²	C₂²
cosocle	C₂³×C₅	C₂³×C₅
hypercenter	C₂³×C₄×C₅	D₅
hypocenter	C₅	C₂×C₅×#95
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂³×C₄×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×#3963	C₂	direct (N × H)
6. C₂²×C₄×C₅²	C₄	semidirect
10. C₂²×C₅×Dic₅	C₄	semidirect
13. C₂×#3963	C₅	direct (N × H)
22. C₂×C₄×C₅²	C₂×C₄	semidirect
26. C₂×C₅×Dic₅	C₂×C₄	semidirect
33. #3963	C₂×C₅	direct (N × H)
58. C₂²×C₄×C₅	Dic₅	semidirect
59. C₂²×C₄×C₅	C₄×C₅	semidirect
64. C₂²×Dic₅	C₄×C₅	semidirect
67. C₂×C₅²	#95	semidirect
102. C₂×C₄×C₅	C₂×Dic₅	semidirect
103. C₂×C₄×C₅	C₂×C₄×C₅	semidirect
107. C₂×Dic₅	C₂×C₄×C₅	semidirect
111. C₅²	C₂×#95	semidirect
153. C₂²×C₄	C₅×Dic₅	semidirect
161. C₂×C₅	#3963	direct (N × H)
162. C₂×C₅	C₅×#95	semidirect
185. C₂×C₄	C₂×C₅×Dic₅	semidirect
187. C₅	C₂×#3963	direct (N × H)
188. C₅	C₂×C₅×#95	semidirect
201. C₂	C₅×#3963	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₅²	2
C₂³×C₅×Dic₅	2
C₅×#3963	2
C₂×C₅×#95	5
C₂×#3963	5

Subgroups — C2×C5×#3963 #13102469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3963 #13102469