Subgroups — C₇×C₁₃×7₋¹⁺² #44530135

Order 31213.

276 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇³×C₁₃	C₇	1	1	yes	maximal, characteristic
2	C₁₃×7₋¹⁺²	C₇	1	49	yes	maximal, direct product factor
3	C₇×C₁₃×C₄₉	C₇	1	7	yes	maximal, complemented
4	C₇×7₋¹⁺²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₇²×C₁₃	—	7	7	no	—
6	C₇²×C₁₃	C₇²	1	7	yes	—
7	C₇²×C₁₃	C₇²	1	1	yes	characteristic
8	C₁₃×C₄₉	C₇²	1	49	yes	complemented
9	C₇³	C₇×C₁₃	1	1	yes	characteristic
10	7₋¹⁺²	C₇×C₁₃	1	49	yes	direct product factor
11	C₇×C₄₉	C₇×C₁₃	1	7	yes	complemented
12	C₇×C₁₃	—	7	7	no	—
13	C₇×C₁₃	7₋¹⁺²	1	7	yes	direct product factor
14	C₇×C₁₃	C₇³	1	1	yes	characteristic
15	C₇²	—	7	7	no	—
16	C₇²	C₇²×C₁₃	1	7	yes	—
17	C₇²	C₇²×C₁₃	1	1	yes	characteristic
18	C₄₉	C₇²×C₁₃	1	49	yes	complemented
19	C₁₃	C₇×7₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	—	7	7	no	—
21	C₇	C₁₃×7₋¹⁺²	1	7	yes	direct product factor
22	C₇	C₇³×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₇²×C₁₃	C₇²
commutator, Frattini, cosocle	C₇	C₇³×C₁₃
prime radical	C₇³×C₁₃	C₇
LCS	G ▷ C₇ ▷ C₁
UCS	C₁ ◁ C₇²×C₁₃ ◁ G

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.