Subgroups — C₄×Dic₁₃₀₆ #35229693

Order 20896.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₃₀₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₆₅₃	C₂	1	1	yes	maximal, characteristic
3	#23782584	C₂	1	2	yes	maximal
4	C₄×Dic₆₅₃	C₂	1	2	yes	maximal
5	C₄²×C₆₅₃	C₂	1	1	yes	maximal, characteristic
6	Dic₁₃₀₆	C₄	1	4	yes	direct product factor
7	C₂×Dic₆₅₃	C₂²	1	2	yes	—
8	C₂×Dic₆₅₃	C₂²	1	2	yes	—
9	C₂×C₄×C₆₅₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₆₅₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₆₅₃	C₂²	1	1	yes	characteristic
12	C₂²×C₆₅₃	C₂³	1	1	yes	characteristic
13	C₄×C₆₅₃	—	2	1	no	—
14	C₄×C₆₅₃	C₂×C₄	1	2	yes	—
15	C₄×C₆₅₃	Q₈	1	2	yes	complemented
16	Dic₆₅₃	—	2	2	no	—
17	Dic₆₅₃	C₂×C₄	1	4	yes	—
18	C₂×C₆₅₃	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₆₅₃	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₆₅₃	#41	1	1	yes	characteristic
21	C₆₅₃	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
22	C₄×Q₈	—	653	1	no	maximal, Sylow
23	C₂×Q₈	—	653	1	no	—
24	C₄⋊C₄	—	653	2	no	—
25	C₄⋊C₄	—	653	1	no	—
26	C₄²	—	653	2	no	—
27	C₄²	D₆₅₃	1	1	yes	characteristic
28	Q₈	—	653	4	no	—
29	C₂×C₄	—	653	2	no	—
30	C₂×C₄	—	653	2	no	—
31	C₂×C₄	C₂×D₆₅₃	1	1	yes	characteristic
32	C₂×C₄	C₂×D₆₅₃	1	1	yes	characteristic
33	C₂×C₄	C₂×D₆₅₃	1	1	yes	characteristic
34	C₂²	C₂²×D₆₅₃	1	1	yes	characteristic
35	C₄	—	2	1	no	—
36	C₄	—	1306	2	no	—
37	C₄	—	653	4	no	—
38	C₄	C₄×D₆₅₃	1	2	yes	—
39	C₄	Dic₁₃₀₆	1	2	yes	direct product factor
40	C₂	C₂×C₄×D₆₅₃	1	1	yes	characteristic
41	C₂	C₂×Dic₁₃₀₆	1	1	yes	characteristic
42	C₂	#23782605	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₆₅₃
commutator	C₂×C₆₅₃	C₂²×C₄
Frattini	C₂²	C₂²×D₆₅₃
Fitting	C₄²×C₆₅₃	C₂
socle, prime radical, cosocle	C₂²×C₆₅₃	C₂³
hypercenter	C₄²	D₆₅₃
hypocenter	C₆₅₃	C₄×Q₈
LCS	G ▷ C₂×C₆₅₃ ▷ C₆₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
6. Dic₁₃₀₆	C₄	direct (N × H)
15. C₄×C₆₅₃	Q₈	semidirect
21. C₆₅₃	C₄×Q₈	semidirect
39. C₄	Dic₁₃₀₆	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×Dic₁₃₀₆	2
C₄⋊Dic₆₅₃	2
#23782584	2
C₄×Dic₆₅₃	2
C₄²×C₆₅₃	2
C₄×Q₈	653

Subgroups — C4×Dic1306 #35229693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₁₃₀₆ #35229693