Subgroups — C₇⋊(C₇⋊#10596815) #43249349

Order 28420.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₁₄₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊(C₇⋊#1181)	—	5	1	no	maximal, Hall
4	C₇⋊#10596815	—	7	8	no	maximal
5	C₇²×D₂₉	—	5	1	no	—
6	C₇×D₁₄₅	D₇	1	8	yes	—
7	C₇²×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₂₉	Dic₇	1	8	yes	complemented
9	C₇⋊(C₇⋊AGL(1,𝔽₅))	—	29	1	no	maximal, Hall
10	C₇⋊#1181	—	35	8	no	—
11	#10596815	—	49	1	no	Hall
12	C₇²×D₅	—	29	1	no	—
13	C₇×D₂₉	—	5	8	no	—
14	D₁₄₅	C₇⋊D₇	1	1	yes	characteristic
15	C₅×C₇²	#1181	1	1	yes	characteristic, complemented, Hall
16	C₇×C₂₉	C₇⋊AGL(1,𝔽₅)	1	8	yes	complemented
17	C₇⋊Dic₇	—	145	1	no	Hall
18	C₅×C₂₉	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
19	C₇⋊AGL(1,𝔽₅)	—	203	8	no	—
20	#1181	—	245	1	no	Hall
21	C₂×C₇²	—	145	1	no	—
22	C₇×D₅	—	29	8	no	—
23	D₂₉	—	5	1	no	—
24	C₇²	#10596815	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₇	C₇⋊#1181	1	8	yes	complemented
26	C₂₉	C₇⋊(C₇⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
27	Dic₇	—	1015	8	no	—
28	AGL(1,𝔽₅)	—	1421	1	no	Hall
29	C₂×C₇	—	145	8	no	—
30	D₅	—	29	1	no	—
31	C₇	C₇⋊#10596815	1	8	yes	complemented
32	C₅	C₇⋊(C₇⋊#1181)	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	7105	1	no	Sylow
34	C₂	—	145	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇²×C₂₉	C₄
prime radical, cosocle	C₇²×D₁₄₅	C₂
LCS	G ▷ C₅×C₇²×C₂₉
UCS	C₁

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.