Subgroups — C₅×#10621725⋊C₇ #37556808

Order 23660.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃²⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃²⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#10621725⋊C₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×#10621725	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₃²⋊C₇	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₁₃²	C₂×C₇	1	1	yes	characteristic
7	C₁₃²⋊C₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₃²	C₄×C₇	1	1	yes	characteristic, complemented, Hall
9	#10621725	C₅×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃²	C₂×C₅×C₇	1	1	yes	characteristic
11	C₅×Dic₁₃	—	91	2	no	—
12	C₁₃²	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
13	C₄×C₅×C₇	—	169	1	no	maximal, Hall
14	C₂×C₅×C₁₃	—	7	2	no	—
15	C₂×C₅×C₇	—	169	1	no	—
16	C₅×C₁₃	—	7	2	no	—
17	Dic₁₃	—	91	2	no	—
18	C₅×C₇	—	169	1	no	Hall
19	C₄×C₇	—	169	1	no	Hall
20	C₂×C₁₃	—	7	2	no	—
21	C₄×C₅	—	1183	1	no	Hall
22	C₂×C₇	—	169	1	no	—
23	C₁₃	—	7	2	no	—
24	C₂×C₅	(C₁₃⋊D₁₃)⋊C₇	1	1	yes	characteristic
25	C₇	—	169	1	no	Sylow
26	C₅	#10621725⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₄	—	1183	1	no	Sylow
28	C₂	C₅×(C₁₃⋊D₁₃)⋊C₇	1	1	yes	characteristic

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.