Subgroups — C₄×#64710 #12014704

Order 1280.

366 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×#64710	C₂	1	2	yes	maximal
3	C₄×#3950	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#672	C₂	1	1	yes	maximal, characteristic
5	#10598213	C₂	1	2	yes	maximal
6	C₂×C₅×#107	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₄×C₅×C₄⋊C₄	—	2	1	no	—
9	C₂×#3950	C₂²	1	2	yes	—
10	C₂²×#672	C₂²	1	1	yes	characteristic
11	C₂²×#672	C₂²	1	1	yes	characteristic
12	C₄×C₄⋊Dic₅	—	2	1	no	—
13	C₅×#340	—	2	1	no	—
14	#64771	—	2	1	no	—
15	#64710	C₄	1	8	yes	direct product factor
16	C₄×#672	C₄	1	4	yes	complemented
17	C₄×#367	—	5	1	no	maximal, Sylow
18	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
19	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₄	—	2	2	no	—
21	C₂×C₄²×C₅	—	4	1	no	—
22	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
23	C₂×C₄⋊Dic₅	—	2	2	no	—
24	C₂×C₄×Dic₅	—	4	1	no	—
25	C₅×#107	—	2	2	no	—
26	C₅×#107	C₂×C₄	1	4	yes	—
27	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
28	C₄×C₅×C₈	Q₈	1	2	yes	—
29	C₅×#95	—	4	1	no	—
30	#3963	—	4	1	no	—
31	#3950	—	2	2	no	—
32	#3950	C₂×C₄	1	4	yes	—
33	C₂×#672	—	2	2	no	—
34	C₂×#672	C₂×C₄	1	2	yes	—
35	C₂×#672	C₂×C₄	1	2	yes	—
36	C₂×#672	C₂×C₄	1	4	yes	—
37	C₂×#367	—	5	2	no	—
38	C₂×C₄×C₁₆	—	5	1	no	—
39	C₄×#107	—	5	1	no	—
40	C₄×#107	D₅	1	1	yes	characteristic
41	#1380	—	5	2	no	—
42	C₂²×C₄×C₅	—	4	2	no	—
43	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
44	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
45	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
46	C₂²×Dic₅	—	4	2	no	—
47	C₂×C₅×C₈	—	2	2	no	—
48	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
49	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
51	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₅×C₈	#41	1	2	yes	—
53	C₅×C₄⋊C₄	—	2	4	no	—
54	C₅×C₄⋊C₄	—	4	2	no	—
55	C₄²×C₅	—	8	2	no	—
56	C₄²×C₅	C₄⋊C₄	1	2	yes	—
57	C₄²×C₅	Q₁₆	1	2	yes	—
58	C₄⋊Dic₅	—	2	4	no	—
59	C₄⋊Dic₅	—	4	2	no	—
60	C₄×Dic₅	—	8	2	no	—
61	#672	—	2	2	no	—
62	#672	C₄²	1	4	yes	complemented
63	C₂²×C₁₆	—	5	1	no	—
64	C₂²×C₁₆	—	5	1	no	—
65	C₂×#107	—	5	2	no	—
66	C₂×#107	C₂×D₅	1	2	yes	—
67	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
68	C₄×C₄⋊C₄	—	2	1	no	—
69	C₄×C₄⋊C₄	—	10	1	no	—
70	#367	—	5	8	no	—
71	C₄×C₁₆	—	5	4	no	—
72	#340	—	2	1	no	—
73	#340	—	10	1	no	—
74	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
75	C₂×C₄×C₅	—	2	2	no	—
76	C₂×C₄×C₅	—	4	4	no	—
77	C₂×C₄×C₅	—	8	2	no	—
78	C₂×C₄×C₅	—	8	2	no	—
79	C₂×C₄×C₅	#107	1	2	yes	—
80	C₂×C₄×C₅	#107	1	2	yes	—
81	C₂×C₄×C₅	SD₃₂	1	2	yes	—
82	C₂×C₄×C₅	SD₃₂	1	2	yes	—
83	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
86	C₂×C₄×C₅	#135	1	2	yes	—
87	C₂×Dic₅	—	4	4	no	—
88	C₂×Dic₅	—	8	2	no	—
89	C₂×Dic₅	—	8	2	no	—
90	C₅×C₈	—	2	2	no	—
91	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
92	C₅×C₈	#117	1	1	yes	characteristic
93	C₅×C₈	C₄×Q₈	1	2	yes	—
94	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
95	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
96	C₂×C₄⋊C₄	—	2	2	no	—
97	C₂×C₄⋊C₄	—	10	2	no	—
98	C₂×C₄²	—	4	1	no	—
99	C₂×C₄²	—	20	1	no	—
100	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
101	C₂×C₁₆	—	5	2	no	—
102	C₂×C₁₆	—	5	4	no	—
103	C₂×C₁₆	—	5	2	no	—
104	C₂×C₁₆	—	10	2	no	—
105	#107	—	2	2	no	—
106	#107	—	5	4	no	—
107	#107	—	10	2	no	—
108	#107	C₄×D₅	1	4	yes	—
109	C₄×C₈	Dic₁₀	1	2	yes	—
110	C₄×C₈	C₄×D₅	1	2	yes	—
111	#95	—	4	1	no	—
112	#95	—	20	1	no	—
113	C₂²×C₅	C₂×#107	1	1	yes	characteristic
114	C₂²×C₅	C₄×D₈	1	2	yes	—
115	C₂²×C₅	C₂×SD₃₂	1	1	yes	characteristic
116	C₂²×C₅	C₂×SD₃₂	1	1	yes	characteristic
117	C₂²×C₅	#508	1	2	yes	—
118	C₄×C₅	—	2	2	no	—
119	C₄×C₅	—	8	4	no	—
120	C₄×C₅	#367	1	4	yes	complemented
121	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
122	C₄×C₅	#427	1	1	yes	characteristic
123	C₄×C₅	C₄×Q₁₆	1	2	yes	—
124	Dic₅	—	8	4	no	—
125	C₂²×C₄	—	4	2	no	—
126	C₂²×C₄	—	20	2	no	—
127	C₂²×C₄	#686	1	1	yes	characteristic
128	C₂²×C₄	#686	1	1	yes	characteristic
129	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
130	C₂×C₈	—	2	2	no	—
131	C₂×C₈	#683	1	2	yes	—
132	C₂×C₈	C₂×Dic₁₀	1	1	yes	characteristic
133	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
134	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
135	C₂×C₈	#709	1	2	yes	—
136	C₄⋊C₄	—	2	4	no	—
137	C₄⋊C₄	—	4	2	no	—
138	C₄⋊C₄	—	10	4	no	—
139	C₄⋊C₄	—	20	2	no	—
140	C₄²	—	8	2	no	—
141	C₄²	—	40	2	no	—
142	C₄²	#683	1	2	yes	—
143	C₄²	#689	1	2	yes	—
144	C₁₆	—	5	4	no	—
145	C₁₆	—	10	2	no	—
146	C₂×C₅	C₄×#107	1	1	yes	characteristic
147	C₂×C₅	C₂×#367	1	1	yes	characteristic
148	C₂×C₅	#2158	1	1	yes	characteristic
149	C₂×C₅	C₄×SD₃₂	1	2	yes	—
150	C₂×C₅	C₄×SD₃₂	1	2	yes	—
151	C₂³	C₂×#686	1	1	yes	characteristic
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	4	4	no	—
154	C₂×C₄	—	8	2	no	—
155	C₂×C₄	—	8	2	no	—
156	C₂×C₄	—	20	4	no	—
157	C₂×C₄	—	40	2	no	—
158	C₂×C₄	—	40	2	no	—
159	C₂×C₄	#3939	1	2	yes	—
160	C₂×C₄	#3939	1	2	yes	—
161	C₂×C₄	#3959	1	2	yes	—
162	C₂×C₄	#3960	1	2	yes	—
163	C₂×C₄	C₂×#683	1	1	yes	characteristic
164	C₂×C₄	C₄×C₂²⋊D₅	1	2	yes	—
165	C₂×C₄	C₂×#689	1	1	yes	characteristic
166	C₂×C₄	#4096	1	2	yes	—
167	C₈	—	2	2	no	—
168	C₈	C₄×Dic₁₀	1	2	yes	—
169	C₈	C₄²×D₅	1	1	yes	characteristic
170	C₈	#4018	1	1	yes	characteristic
171	C₅	C₄×#367	1	1	yes	characteristic, complemented, Sylow
172	C₂²	C₂×#3939	1	1	yes	characteristic
173	C₂²	C₄×#686	1	2	yes	—
174	C₂²	C₂×#3959	1	1	yes	characteristic
175	C₂²	C₂×#3960	1	1	yes	characteristic
176	C₂²	#65483	1	2	yes	—
177	C₄	—	2	2	no	—
178	C₄	—	8	4	no	—
179	C₄	—	40	4	no	—
180	C₄	#64710	1	4	yes	direct product factor
181	C₄	C₄×#683	1	1	yes	characteristic
182	C₄	#65287	1	1	yes	characteristic
183	C₄	C₄×#689	1	2	yes	—
184	C₂	C₄×#3939	1	1	yes	characteristic
185	C₂	C₂×#64710	1	1	yes	characteristic
186	C₂	#10601441	1	1	yes	characteristic
187	C₂	C₄×#3959	1	2	yes	—
188	C₂	C₄×#3960	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	#686
commutator	C₅×C₈	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₅
Fitting	C₄×C₅×#107	C₂
socle, prime radical	C₂³×C₅	C₂×D₈
cosocle	C₂²×C₅×C₈	C₂³
hypercenter	C₄×#107	D₅
hypocenter	C₅	C₄×#367
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
15. #64710	C₄	direct (N × H)
16. C₄×#672	C₄	semidirect
62. #672	C₄²	semidirect
120. C₄×C₅	#367	semidirect
171. C₅	C₄×#367	semidirect
180. C₄	#64710	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×#107	2
C₂×#64710	2
C₄×#3950	2
C₂×C₄×#672	2
#10598213	2
C₄×#367	5

Subgroups — C4×#64710 #12014704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#64710 #12014704