Subgroups — C₇⋊#16810007 #37556875

Order 23660.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₅×C₁₃²	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊#10621725	—	5	1	no	maximal, Hall
4	#16810007	—	7	1	no	maximal, Hall
5	C₂×C₇×C₁₃²	—	5	1	no	—
6	C₇⋊#63120	—	13	14	no	maximal
7	D₅×C₁₃²	D₇	1	1	yes	characteristic
8	C₇×C₁₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
9	C₇×D₅×C₁₃	D₁₃	1	14	yes	—
10	C₅×C₁₃²	Dic₇	1	1	yes	characteristic, complemented, Hall
11	#10621725	—	35	1	no	Hall
12	C₅×C₇×C₁₃	Dic₁₃	1	14	yes	complemented
13	Dic₉₁	—	65	14	no	—
14	C₂×C₁₃²	—	5	1	no	—
15	#63120	—	91	14	no	—
16	C₂×C₇×C₁₃	—	5	14	no	—
17	C₁₃²	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
18	C₇⋊AGL(1,𝔽₅)	—	169	1	no	Hall
19	D₅×C₁₃	D₉₁	1	14	yes	—
20	C₇×C₁₃	#63120	1	14	yes	complemented
21	C₇×D₅	C₁₃⋊D₁₃	1	1	yes	characteristic
22	C₅×C₁₃	Dic₉₁	1	14	yes	complemented
23	Dic₁₃	—	455	14	no	—
24	C₅×C₇	#10621725	1	1	yes	characteristic, complemented, Hall
25	Dic₇	—	845	1	no	Hall
26	C₂×C₁₃	—	5	14	no	—
27	AGL(1,𝔽₅)	—	1183	1	no	Hall
28	C₂×C₇	—	5	1	no	—
29	C₁₃	C₇⋊#63120	1	14	yes	complemented
30	D₅	C₇⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
31	C₇	#16810007	1	1	yes	characteristic, complemented, Sylow
32	C₅	C₇⋊#10621725	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	5915	1	no	Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇×C₁₃²	C₄
prime radical, cosocle	C₇×D₅×C₁₃²	C₂
LCS	G ▷ C₅×C₇×C₁₃²
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.