Subgroups — C₄×#64725 #12014703

Order 1280.

366 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#64725	C₂	1	2	yes	maximal
3	C₄×#3950	C₂	1	2	yes	maximal
4	#10598297	C₂	1	2	yes	maximal
5	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
6	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×#3950	C₂²	1	4	yes	—
9	C₄×C₄⋊Dic₅	—	2	2	no	—
10	C₄×C₅×C₁₆	C₄	1	4	yes	complemented
11	#64771	—	2	2	no	—
12	#64725	C₄	1	8	yes	direct product factor
13	C₄×#367	—	5	1	no	maximal, Sylow
14	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
15	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
17	C₂×C₄⋊Dic₅	—	2	4	no	—
18	C₂×C₄×Dic₅	—	4	2	no	—
19	C₂×C₅×C₁₆	—	2	2	no	—
20	C₂×C₅×C₁₆	C₂×C₄	1	4	yes	—
21	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
23	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
24	C₄×C₅×C₈	Q₈	1	2	yes	—
25	#3963	—	4	2	no	—
26	#3950	—	2	4	no	—
27	#3950	C₂×C₄	1	8	yes	—
28	C₂×#367	—	5	2	no	—
29	C₂×C₄×C₁₆	D₅	1	1	yes	characteristic
30	C₄×#107	—	5	2	no	—
31	#1380	—	5	2	no	—
32	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
33	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
34	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
35	C₂²×Dic₅	—	4	4	no	—
36	C₂×C₅×C₈	—	2	2	no	—
37	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
38	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
39	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₅×C₈	#41	1	2	yes	—
42	C₄²×C₅	C₄⋊C₄	1	2	yes	—
43	C₄²×C₅	Q₁₆	1	2	yes	—
44	C₄⋊Dic₅	—	2	8	no	—
45	C₄⋊Dic₅	—	4	4	no	—
46	C₄×Dic₅	—	8	4	no	—
47	C₅×C₁₆	—	2	2	no	—
48	C₅×C₁₆	C₄²	1	4	yes	complemented
49	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic
50	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic
51	C₂×#107	—	5	4	no	—
52	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
53	C₄×C₄⋊C₄	—	10	2	no	—
54	#367	—	5	8	no	—
55	C₄×C₁₆	Dic₅	1	4	yes	complemented
56	#340	—	10	2	no	—
57	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
58	C₂×C₄×C₅	—	2	2	no	—
59	C₂×C₄×C₅	#107	1	2	yes	—
60	C₂×C₄×C₅	#107	1	2	yes	—
61	C₂×C₄×C₅	SD₃₂	1	4	yes	—
62	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
64	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
65	C₂×C₄×C₅	#135	1	2	yes	—
66	C₂×Dic₅	—	4	8	no	—
67	C₂×Dic₅	—	8	4	no	—
68	C₂×Dic₅	—	8	4	no	—
69	C₅×C₈	—	2	2	no	—
70	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
71	C₅×C₈	#117	1	1	yes	characteristic
72	C₅×C₈	C₄×Q₈	1	2	yes	—
73	C₂²×C₈	D₂₀	1	1	yes	characteristic
74	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
75	C₂×C₄⋊C₄	—	10	4	no	—
76	C₂×C₄²	—	20	2	no	—
77	C₂×C₄²	D₂₀	1	1	yes	characteristic
78	C₂×C₁₆	—	2	2	no	—
79	C₂×C₁₆	C₄×D₅	1	4	yes	—
80	C₂×C₁₆	C₂×Dic₅	1	2	yes	—
81	C₂×C₁₆	C₂×Dic₅	1	2	yes	—
82	#107	—	5	8	no	—
83	#107	—	10	4	no	—
84	C₄×C₈	Dic₁₀	1	2	yes	—
85	C₄×C₈	C₂×Dic₅	1	2	yes	—
86	#95	—	20	2	no	—
87	C₂²×C₅	C₂×#107	1	1	yes	characteristic
88	C₂²×C₅	C₄×D₈	1	2	yes	—
89	C₂²×C₅	C₂×SD₃₂	1	2	yes	—
90	C₂²×C₅	#508	1	2	yes	—
91	C₄×C₅	—	2	2	no	—
92	C₄×C₅	#367	1	4	yes	complemented
93	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
94	C₄×C₅	#427	1	1	yes	characteristic
95	C₄×C₅	C₄×Q₁₆	1	2	yes	—
96	Dic₅	—	8	8	no	—
97	C₂²×C₄	—	20	4	no	—
98	C₂²×C₄	D₄₀	1	1	yes	characteristic
99	C₂²×C₄	D₄₀	1	1	yes	characteristic
100	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
101	C₂×C₈	—	2	2	no	—
102	C₂×C₈	C₄⋊Dic₅	1	2	yes	—
103	C₂×C₈	C₂×Dic₁₀	1	1	yes	characteristic
104	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
105	C₂×C₈	#709	1	2	yes	—
106	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
107	C₄⋊C₄	—	10	8	no	—
108	C₄⋊C₄	—	20	4	no	—
109	C₄²	—	40	4	no	—
110	C₄²	Dic₂₀	1	2	yes	—
111	C₄²	C₄⋊Dic₅	1	2	yes	—
112	C₁₆	—	2	2	no	—
113	C₁₆	C₄×Dic₅	1	4	yes	complemented
114	C₂×C₅	C₄×#107	1	1	yes	characteristic
115	C₂×C₅	C₂×#367	1	1	yes	characteristic
116	C₂×C₅	#2158	1	1	yes	characteristic
117	C₂×C₅	C₄×SD₃₂	1	4	yes	—
118	C₂³	C₂×D₄₀	1	1	yes	characteristic
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	20	8	no	—
121	C₂×C₄	—	40	4	no	—
122	C₂×C₄	—	40	4	no	—
123	C₂×C₄	#3932	1	4	yes	—
124	C₂×C₄	#3950	1	2	yes	—
125	C₂×C₄	#3950	1	2	yes	—
126	C₂×C₄	C₄×D₂₀	1	2	yes	—
127	C₂×C₄	#4050	1	2	yes	—
128	C₂×C₄	C₂×Dic₂₀	1	1	yes	characteristic
129	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
130	C₈	—	2	2	no	—
131	C₈	C₄×Dic₁₀	1	2	yes	—
132	C₈	C₂×C₄×Dic₅	1	1	yes	characteristic
133	C₈	#4072	1	1	yes	characteristic
134	C₅	C₄×#367	1	1	yes	characteristic, complemented, Sylow
135	C₂²	C₄×D₄₀	1	2	yes	—
136	C₂²	C₂×#3932	1	2	yes	—
137	C₂²	#65193	1	2	yes	—
138	C₂²	C₂×#3950	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	40	8	no	—
141	C₄	#64725	1	4	yes	direct product factor
142	C₄	C₄×Dic₂₀	1	2	yes	—
143	C₄	C₄×C₄⋊Dic₅	1	1	yes	characteristic
144	C₄	#65395	1	1	yes	characteristic
145	C₂	C₄×#3932	1	4	yes	—
146	C₂	C₄×#3950	1	1	yes	characteristic
147	C₂	C₂×#64725	1	1	yes	characteristic
148	C₂	#10602197	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄₀
commutator	C₅×C₈	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₅
Fitting	C₂×C₄×C₅×C₁₆	C₂
socle, prime radical	C₂³×C₅	C₂×D₈
cosocle	C₂²×C₅×C₈	C₂³
hypercenter	C₂×C₄×C₁₆	D₅
hypocenter	C₅	C₄×#367
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
10. C₄×C₅×C₁₆	C₄	semidirect
12. #64725	C₄	direct (N × H)
48. C₅×C₁₆	C₄²	semidirect
55. C₄×C₁₆	Dic₅	semidirect
92. C₄×C₅	#367	semidirect
113. C₁₆	C₄×Dic₅	semidirect
134. C₅	C₄×#367	semidirect
141. C₄	#64725	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×C₄×C₅×C₁₆	2
C₂×#64725	2
C₄×#3950	2
#10598297	2
C₄×#367	5

Subgroups — C4×#64725 #12014703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#64725 #12014703