Subgroups — #37556809

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	#17990042	—	5	1	no	maximal, Hall
4	C₁₃×Dic₆₅	—	7	1	no	maximal, Hall
5	C₂×C₁₃²⋊C₇	D₅	1	1	yes	characteristic
6	C₂×C₅×C₁₃²	D₇	1	1	yes	characteristic
7	C₁₃²⋊C₇	Dic₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₃²	Dic₇	1	1	yes	characteristic, complemented, Hall
9	C₁₃×Dic₁₃	—	35	1	no	Hall
10	C₂×C₁₃²	D₃₅	1	1	yes	characteristic
11	Dic₆₅	—	7	1	no	—
12	C₁₃×Dic₅	—	91	1	no	—
13	C₁₃²	Dic₃₅	1	1	yes	characteristic, complemented, Sylow
14	Dic₃₅	—	169	1	no	maximal, Hall
15	C₂×C₅×C₁₃	—	14	1	no	—
16	C₂×C₅×C₁₃	—	14	1	no	—
17	C₂×C₅×C₇	—	338	1	no	—
18	C₅×C₁₃	—	14	1	no	—
19	C₅×C₁₃	—	14	1	no	—
20	C₄×C₁₃	—	455	1	no	—
21	Dic₁₃	—	35	1	no	—
22	C₅×C₇	—	338	1	no	Hall
23	Dic₇	—	845	1	no	Hall
24	C₂×C₁₃	—	14	1	no	—
25	C₂×C₁₃	—	14	1	no	—
26	Dic₅	—	91	1	no	Hall
27	C₂×C₇	—	338	1	no	—
28	C₁₃	—	14	1	no	—
29	C₁₃	—	14	1	no	—
30	C₂×C₅	#14556975	1	1	yes	characteristic
31	C₇	—	338	1	no	Sylow
32	C₅	#17990042	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	455	1	no	Sylow
34	C₂	C₅⋊#14556975	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊#14556975
commutator, hypocenter	C₅×C₁₃²⋊C₇	C₄
Fitting, socle	C₂×C₅×C₁₃²	D₇
prime radical, cosocle	C₂×C₅×C₁₃²⋊C₇	C₂
LCS	G ▷ C₅×C₁₃²⋊C₇
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.