Subgroups — C₁₃×#17309 #15703648

Order 3328.

1466 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1446	C₂	1	15	yes	maximal
2	C₂³×Q₈×C₁₃	C₂²	1	5	yes	—
3	C₂×C₁₃×#95	C₂²	1	30	yes	—
4	C₂²×Q₈×C₁₃	—	4	30	no	—
5	C₂²×Q₈×C₁₃	Q₈	1	20	yes	complemented
6	C₂³×C₄×C₁₃	C₂³	1	15	yes	—
7	C₁₃×#95	—	4	30	no	—
8	#17309	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
10	C₂×Q₈×C₁₃	—	4	60	no	—
11	C₂×Q₈×C₁₃	—	4	80	no	—
12	C₂²×C₄×C₁₃	—	2	90	no	—
13	C₂²×C₄×C₁₃	C₂×Q₈	1	30	yes	—
14	#1446	C₂×C₁₃	1	15	yes	—
15	C₂³×C₁₃	C₂²×Q₈	1	5	yes	—
16	C₂³×C₁₃	H(5,𝔽₂)	1	10	yes	—
17	Q₈×C₁₃	—	4	80	no	—
18	C₂×C₄×C₁₃	—	2	90	no	—
19	C₂×C₄×C₁₃	—	4	60	no	—
20	C₂³×Q₈	C₂²×C₁₃	1	5	yes	—
21	C₂×#95	C₂²×C₁₃	1	30	yes	—
22	C₂²×C₁₃	#543	1	15	yes	—
23	C₂²×C₁₃	Q₈²	1	10	yes	—
24	C₂²×C₁₃	H(3,𝔽₄)	1	10	yes	—
25	C₄×C₁₃	—	4	30	no	—
26	C₂²×Q₈	—	4	30	no	—
27	C₂²×Q₈	Q₈×C₁₃	1	20	yes	complemented
28	C₂³×C₄	C₂³×C₁₃	1	15	yes	—
29	#95	—	4	30	no	—
30	C₂×C₁₃	#2811	1	10	yes	—
31	C₂×C₁₃	#2840	1	5	yes	—
32	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
33	C₂×Q₈	—	4	60	no	—
34	C₂×Q₈	—	4	80	no	—
35	C₂²×C₄	—	2	90	no	—
36	C₂²×C₄	C₂×Q₈×C₁₃	1	30	yes	—
37	C₁₃	#17309	1	1	yes	characteristic, direct product factor, Sylow
38	C₂³	C₂²×Q₈×C₁₃	1	5	yes	—
39	C₂³	C₁₃×H(5,𝔽₂)	1	10	yes	—
40	Q₈	—	4	80	no	—
41	C₂×C₄	—	2	90	no	—
42	C₂×C₄	—	4	60	no	—
43	C₂²	C₁₃×#543	1	15	yes	—
44	C₂²	Q₈²×C₁₃	1	10	yes	—
45	C₂²	C₁₃×H(3,𝔽₄)	1	10	yes	—
46	C₄	—	4	30	no	—
47	C₂	C₁₃×#2811	1	10	yes	—
48	C₂	C₁₃×#2840	1	5	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₂²×Q₈×C₁₃	Q₈	semidirect
8. #17309	C₁₃	direct (N × H)
27. C₂²×Q₈	Q₈×C₁₃	semidirect
37. C₁₃	#17309	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#1446	2
#17309	13

Subgroups — C13×#17309 #15703648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17309 #15703648