Subgroups — C₂²×C₅×D₄₉ #14519940

Order 1960.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₄₉	C₂	1	6	yes	maximal, direct product factor
3	C₂×C₅×C₄₉	C₂²	1	3	yes	complemented
4	C₅×D₄₉	C₂²	1	4	yes	direct product factor
5	C₂²×D₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₅×D₇	—	7	1	no	maximal
7	C₅×C₄₉	C₂³	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×D₄₉	C₂×C₅	1	6	yes	direct product factor
10	C₂²×C₅×C₇	D₇	1	1	yes	characteristic
11	C₂×C₅×D₇	—	7	6	no	—
12	C₂×C₄₉	C₂²×C₅	1	3	yes	complemented
13	D₄₉	C₂²×C₅	1	4	yes	direct product factor
14	C₂×C₅×C₇	C₂×D₇	1	3	yes	—
15	C₅×D₇	—	7	4	no	—
16	C₂²×D₇	—	7	1	no	—
17	C₄₉	C₂³×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₂³×C₅	—	49	1	no	Hall
19	C₅×C₇	C₂²×D₇	1	1	yes	characteristic
20	C₂²×C₇	C₅×D₇	1	1	yes	characteristic
21	C₂×D₇	—	7	6	no	—
22	C₂²×C₅	—	49	6	no	—
23	C₂²×C₅	D₄₉	1	1	yes	characteristic, direct product factor
24	C₂×C₇	C₂×C₅×D₇	1	3	yes	—
25	D₇	—	7	4	no	—
26	C₂×C₅	—	49	4	no	—
27	C₂×C₅	C₂×D₄₉	1	3	yes	direct product factor
28	C₂³	—	49	1	no	Sylow
29	C₇	C₂²×C₅×D₇	1	1	yes	characteristic
30	C₅	C₂²×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²	—	49	6	no	—
32	C₂²	C₅×D₄₉	1	1	yes	characteristic, direct product factor
33	C₂	—	49	4	no	—
34	C₂	C₂×C₅×D₄₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂³×C₅
Frattini	C₇	C₂²×C₅×D₇
Fitting	C₂²×C₅×C₄₉	C₂
socle	C₂²×C₅×C₇	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂²×C₅

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

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