Subgroups — C₂₉×#17309 #20312209

Order 7424.

1466 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#1446	C₂	1	15	yes	maximal
2	C₂³×Q₈×C₂₉	C₂²	1	5	yes	—
3	C₂×C₂₉×#95	C₂²	1	30	yes	—
4	C₂²×Q₈×C₂₉	—	4	30	no	—
5	C₂²×Q₈×C₂₉	Q₈	1	20	yes	complemented
6	C₂³×C₄×C₂₉	C₂³	1	15	yes	—
7	C₂₉×#95	—	4	30	no	—
8	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
9	C₂×Q₈×C₂₉	—	4	60	no	—
10	C₂×Q₈×C₂₉	—	4	80	no	—
11	C₂²×C₄×C₂₉	—	2	90	no	—
12	C₂²×C₄×C₂₉	C₂×Q₈	1	30	yes	—
13	#17309	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂³×C₂₉	C₂²×Q₈	1	5	yes	—
15	C₂³×C₂₉	H(5,𝔽₂)	1	10	yes	—
16	Q₈×C₂₉	—	4	80	no	—
17	C₂×C₄×C₂₉	—	2	90	no	—
18	C₂×C₄×C₂₉	—	4	60	no	—
19	#1446	C₂×C₂₉	1	15	yes	—
20	C₂²×C₂₉	#543	1	15	yes	—
21	C₂²×C₂₉	Q₈²	1	10	yes	—
22	C₂²×C₂₉	H(3,𝔽₄)	1	10	yes	—
23	C₄×C₂₉	—	4	30	no	—
24	C₂³×Q₈	C₂²×C₂₉	1	5	yes	—
25	C₂×#95	C₂²×C₂₉	1	30	yes	—
26	C₂×C₂₉	#2811	1	10	yes	—
27	C₂×C₂₉	#2840	1	5	yes	—
28	C₂²×Q₈	—	4	30	no	—
29	C₂²×Q₈	Q₈×C₂₉	1	20	yes	complemented
30	C₂³×C₄	C₂³×C₂₉	1	15	yes	—
31	#95	—	4	30	no	—
32	C₂₉	#17309	1	1	yes	characteristic, direct product factor, Sylow
33	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
34	C₂×Q₈	—	4	60	no	—
35	C₂×Q₈	—	4	80	no	—
36	C₂²×C₄	—	2	90	no	—
37	C₂²×C₄	C₂×Q₈×C₂₉	1	30	yes	—
38	C₂³	C₂²×Q₈×C₂₉	1	5	yes	—
39	C₂³	C₂₉×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	C₂₉×#543	1	15	yes	—
44	C₂²	Q₈²×C₂₉	1	10	yes	—
45	C₂²	C₂₉×H(3,𝔽₄)	1	10	yes	—
46	C₄	—	4	30	no	—
47	C₂	C₂₉×#2811	1	10	yes	—
48	C₂	C₂₉×#2840	1	5	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₂₉
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₂²×Q₈×C₂₉	Q₈	semidirect
13. #17309	C₂₉	direct (N × H)
29. C₂²×Q₈	Q₈×C₂₉	semidirect
32. C₂₉	#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
C₂₉×#1446	2
#17309	29

Subgroups — C29×#17309 #20312209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#17309 #20312209