Subgroups — C₂×((C₂⁴⋊C₅)⋊C₂)⋊C₃ #11757165

Order 960.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
2	((C₂⁴⋊C₅)⋊C₂)⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×(C₂⁴⋊C₅)⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	AGL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
5	C₂×#120⋊C₃	—	5	1	no	maximal, Hall
6	C₂×C₂⁴⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
7	(C₂⁴⋊C₅)⋊C₂	C₂×C₃	1	2	yes	complemented
8	C₂×C₂²⋊A₄	D₅	1	1	yes	characteristic, complemented
9	#120⋊C₃	—	5	2	no	—
10	C₂⁴⋊C₅	C₂²×C₃	1	1	yes	characteristic, complemented
11	C₂×#120	—	5	1	no	Sylow
12	C₂×C₃×D₅	—	16	1	no	maximal
13	C₂²⋊A₄	C₂×D₅	1	1	yes	characteristic, complemented
14	C₂²×A₄	—	20	1	no	—
15	C₂⁵	C₃×D₅	1	1	yes	characteristic, complemented
16	C₂²×D₄	—	15	1	no	—
17	#120	—	5	2	no	—
18	#120	—	15	2	no	—
19	C₂×C₂²⋊C₄	—	15	1	no	—
20	C₂×C₃×C₅	—	16	1	no	—
21	C₃×D₅	—	16	2	no	—
22	C₂×A₄	—	20	1	no	—
23	C₂×A₄	—	20	2	no	—
24	C₂×D₅	—	16	1	no	—
25	C₂⁴	—	5	1	no	—
26	C₂⁴	—	15	1	no	—
27	C₂⁴	—	15	1	no	—
28	C₂⁴	C₂×C₃×D₅	1	1	yes	characteristic, complemented
29	C₂×D₄	—	15	2	no	—
30	C₂×D₄	—	15	2	no	—
31	C₂×D₄	—	30	2	no	—
32	C₂×D₄	—	30	2	no	—
33	C₂²×C₄	—	15	1	no	—
34	C₂²⋊C₄	—	15	2	no	—
35	C₂²⋊C₄	—	15	2	no	—
36	C₃×C₅	—	16	1	no	Hall
37	C₂²×C₃	—	80	1	no	—
38	A₄	—	20	1	no	—
39	C₂×C₅	—	16	1	no	—
40	D₅	—	16	2	no	—
41	C₂³	—	5	1	no	—
42	C₂³	—	5	2	no	—
43	C₂³	—	15	1	no	—
44	C₂³	—	15	1	no	—
45	C₂³	—	15	2	no	—
46	C₂³	—	15	2	no	—
47	C₂³	—	30	2	no	—
48	C₂³	—	30	1	no	—
49	C₂³	—	30	1	no	—
50	D₄	—	30	4	no	—
51	D₄	—	30	4	no	—
52	C₂×C₄	—	15	2	no	—
53	C₂×C₄	—	30	1	no	—
54	C₂×C₄	—	30	1	no	—
55	C₂×C₃	—	16	1	no	—
56	C₂×C₃	—	80	2	no	—
57	C₅	—	16	1	no	Sylow
58	C₂²	—	5	1	no	—
59	C₂²	—	15	2	no	—
60	C₂²	—	15	1	no	—
61	C₂²	—	15	2	no	—
62	C₂²	—	15	1	no	—
63	C₂²	—	20	1	no	—
64	C₂²	—	30	2	no	—
65	C₂²	—	30	2	no	—
66	C₂²	—	60	1	no	—
67	C₄	—	30	2	no	—
68	C₃	—	16	1	no	Sylow
69	C₂	—	15	1	no	—
70	C₂	—	15	1	no	—
71	C₂	—	20	2	no	—
72	C₂	((C₂⁴⋊C₅)⋊C₂)⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	((C₂⁴⋊C₅)⋊C₂)⋊C₃
commutator, cosocle, hypocenter	C₂⁴⋊C₅	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂⁵	C₃×D₅
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×AGL(1,𝔽₁₆)	C₂	semidirect
2. ((C₂⁴⋊C₅)⋊C₂)⋊C₃	C₂	direct (N × H)
3. C₂×(C₂⁴⋊C₅)⋊C₂	C₃	semidirect
4. AGL(1,𝔽₁₆)	C₂²	semidirect
6. C₂×C₂⁴⋊C₅	C₂×C₃	semidirect
7. (C₂⁴⋊C₅)⋊C₂	C₂×C₃	semidirect
8. C₂×C₂²⋊A₄	D₅	semidirect
10. C₂⁴⋊C₅	C₂²×C₃	semidirect
13. C₂²⋊A₄	C₂×D₅	semidirect
15. C₂⁵	C₃×D₅	semidirect
28. C₂⁴	C₂×C₃×D₅	semidirect
72. C₂	((C₂⁴⋊C₅)⋊C₂)⋊C₃	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×AGL(1,𝔽₁₆)	2
((C₂⁴⋊C₅)⋊C₂)⋊C₃	2
C₂×(C₂⁴⋊C₅)⋊C₂	3
C₂×#120⋊C₃	5
C₂×C₃×D₅	16

Subgroups — C2×((C24⋊C5)⋊C2)⋊C3 #11757165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×((C₂⁴⋊C₅)⋊C₂)⋊C₃ #11757165