Subgroups — C₇×#14556975 #30658564

Order 16562.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃²⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₃×D₁₃	—	7	1	no	maximal
3	#14556975	C₇	1	1	yes	maximal, characteristic, direct product factor
4	C₇×C₁₃²	D₇	1	1	yes	characteristic, complemented
5	C₁₃²⋊C₇	—	2	3	no	—
6	C₁₃²⋊C₇	C₂×C₇	1	1	yes	characteristic, complemented
7	C₁₃×D₁₃	—	7	1	no	Hall
8	C₂×C₇×C₁₃	—	91	1	no	—
9	C₇×D₁₃	—	7	1	no	—
10	C₁₃²	C₇×D₇	1	1	yes	characteristic, complemented, Sylow
11	C₇×D₇	—	169	1	no	maximal, Hall
12	C₇×C₁₃	—	14	1	no	—
13	C₇×C₁₃	—	14	1	no	—
14	C₇²	—	338	1	no	Sylow
15	C₂×C₁₃	—	91	1	no	—
16	D₁₃	—	7	1	no	—
17	C₂×C₇	—	91	1	no	—
18	D₇	—	169	1	no	—
19	C₁₃	—	7	1	no	—
20	C₁₃	—	14	1	no	—
21	C₇	—	338	1	no	—
22	C₇	—	338	3	no	—
23	C₇	#14556975	1	1	yes	characteristic, direct product factor
24	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	#14556975
commutator, cosocle, hypocenter	C₁₃²⋊C₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃²	D₇
LCS	G ▷ C₁₃²⋊C₇
UCS	C₁ ◁ C₇

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.