Subgroups — #16810010⋊C₇ #37556839

Order 23660.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×(C₁₃⋊D₁₃)⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃²⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#10621728⋊C₇	—	5	1	no	maximal, Hall
4	#16810010	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	(C₁₃⋊D₁₃)⋊C₇	D₅	1	1	yes	characteristic
6	C₅×C₁₃⋊D₁₃	C₂×C₇	1	1	yes	characteristic
7	C₁₃²⋊C₇	Dic₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₃²	C₄×C₇	1	1	yes	characteristic, complemented, Hall
9	#10621728	—	5	1	no	Hall
10	C₁₃⋊D₁₃	C₇×D₅	1	1	yes	characteristic
11	#63118	—	91	2	no	—
12	C₁₃²	C₇×Dic₅	1	1	yes	characteristic, complemented, Sylow
13	C₇×Dic₅	—	169	1	no	maximal, Hall
14	C₅×D₁₃	—	91	2	no	—
15	C₂×C₅×C₇	—	169	1	no	—
16	C₅×C₁₃	—	7	2	no	—
17	#261	—	455	2	no	—
18	C₅×C₇	—	169	1	no	Hall
19	C₄×C₇	—	845	1	no	Hall
20	D₁₃	—	91	2	no	—
21	Dic₅	—	1183	1	no	Hall
22	C₂×C₇	—	169	1	no	—
23	C₁₃	—	7	2	no	—
24	C₂×C₅	—	1183	1	no	—
25	C₇	—	169	1	no	Sylow
26	C₅	#10621728⋊C₇	1	1	yes	characteristic, complemented, Sylow
27	C₄	—	5915	1	no	Sylow
28	C₂	—	169	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃²	C₄×C₇
prime radical	C₅×(C₁₃⋊D₁₃)⋊C₇	C₂
cosocle	C₅×C₁₃⋊D₁₃	C₂×C₇
LCS	G ▷ C₅×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.