Subgroups — C₇⋊#16814867 #39905967

Order 25900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₇×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₂₉₅	—	5	6	no	maximal
4	#16814867	—	7	1	no	maximal, Hall
5	C₂×C₅×C₇×C₃₇	D₅	1	6	yes	—
6	C₂×C₅²×C₃₇	D₇	1	1	yes	characteristic
7	C₅×C₇×C₃₇	Dic₅	1	6	yes	complemented
8	Dic₂₅₉	—	25	1	no	Hall
9	C₅²×C₃₇	Dic₇	1	1	yes	characteristic, complemented, Hall
10	Dic₁₈₅	—	35	6	no	—
11	C₇⋊#1039	—	37	1	no	maximal, Hall
12	C₂×C₇×C₃₇	C₅⋊D₅	1	1	yes	characteristic
13	C₂×C₅×C₃₇	D₃₅	1	6	yes	—
14	C₂×C₅²×C₇	D₃₇	1	1	yes	characteristic
15	C₇×C₃₇	#1039	1	1	yes	characteristic, complemented, Hall
16	C₅×C₃₇	Dic₃₅	1	6	yes	complemented
17	C₅²×C₇	Dic₃₇	1	1	yes	characteristic, complemented, Hall
18	Dic₃₇	—	175	1	no	Hall
19	Dic₃₅	—	185	6	no	—
20	#1039	—	259	1	no	Hall
21	C₂×C₃₇	C₅⋊D₃₅	1	1	yes	characteristic
22	C₂×C₅×C₇	D₁₈₅	1	6	yes	—
23	C₂×C₅²	D₂₅₉	1	1	yes	characteristic
24	C₃₇	C₇⋊#1039	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₇	Dic₁₈₅	1	6	yes	complemented
26	Dic₇	—	925	1	no	Hall
27	C₅²	Dic₂₅₉	1	1	yes	characteristic, complemented, Sylow
28	Dic₅	—	1295	6	no	—
29	C₂×C₇	C₅⋊D₁₈₅	1	1	yes	characteristic
30	C₂×C₅	D₁₂₉₅	1	6	yes	—
31	C₇	#16814867	1	1	yes	characteristic, complemented, Sylow
32	C₅	Dic₁₂₉₅	1	6	yes	complemented
33	C₄	—	6475	1	no	Sylow
34	C₂	C₅⋊D₁₂₉₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊D₁₂₉₅
commutator, hypocenter	C₅²×C₇×C₃₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅²×C₇×C₃₇	C₂
LCS	G ▷ C₅²×C₇×C₃₇
UCS	C₁ ◁ C₂

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.