Subgroups — C₇⋊#16814855 #39905949

Order 25900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₉₂₅	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊#10625192	—	5	1	no	maximal
4	#16814855	—	7	1	no	maximal, Hall
5	C₇×D₁₈₅	—	5	1	no	—
6	D₉₂₅	D₇	1	1	yes	characteristic
7	C₅×C₇×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic
8	C₇⋊#3866	—	25	1	no	Hall
9	C₂₅×C₃₇	Dic₇	1	1	yes	characteristic, complemented, Hall
10	#10625192	—	35	1	no	—
11	C₇⋊#1035	—	37	1	no	maximal, Hall
12	C₇×D₃₇	—	25	1	no	—
13	D₁₈₅	—	5	1	no	—
14	C₇×D₂₅	—	37	1	no	—
15	C₇×C₃₇	#1035	1	1	yes	characteristic, complemented, Hall
16	C₅×C₃₇	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic
17	C₇×C₂₅	#3866	1	1	yes	characteristic, complemented, Hall
18	#3866	—	175	1	no	Hall
19	C₇⋊AGL(1,𝔽₅)	—	185	1	no	—
20	#1035	—	259	1	no	Hall
21	D₃₇	—	25	1	no	—
22	C₇×D₅	—	185	1	no	—
23	D₂₅	—	37	1	no	—
24	C₃₇	C₇⋊#1035	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₇	#10625192	1	1	yes	characteristic
26	Dic₇	—	925	1	no	Hall
27	C₂₅	C₇⋊#3866	1	1	yes	characteristic, complemented, Sylow
28	AGL(1,𝔽₅)	—	1295	1	no	—
29	C₂×C₇	—	925	1	no	—
30	D₅	—	185	1	no	—
31	C₇	#16814855	1	1	yes	characteristic, complemented, Sylow
32	C₅	C₇⋊#10625192	1	1	yes	characteristic
33	C₄	—	6475	1	no	Sylow
34	C₂	—	925	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₇×C₂₅×C₃₇	C₄
Frattini	C₅	C₇⋊#10625192
socle	C₅×C₇×C₃₇	AGL(1,𝔽₅)
prime radical, cosocle	C₇×D₉₂₅	C₂
LCS	G ▷ C₇×C₂₅×C₃₇
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.