Subgroups — #90807

Order 464.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₂₉	C₂	1	2	yes	maximal, complemented
3	C₂×Dic₂₉	C₂	1	2	yes	maximal, complemented
4	C₄×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₅₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₉	C₂²	1	2	yes	—
7	C₂×D₂₉	C₂²	1	1	yes	characteristic
8	C₄×C₂₉	C₂²	1	1	yes	characteristic
9	Dic₂₉	C₂²	1	2	yes	—
10	Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₂₉	—	2	2	no	—
12	C₂×C₂₉	C₂³	1	1	yes	characteristic
13	D₂₉	—	2	1	no	—
14	C₂₉	#41	1	1	yes	characteristic, complemented, Sylow
15	#41	—	29	1	no	maximal, Sylow
16	Q₈	—	29	1	no	—
17	D₄	—	29	2	no	—
18	D₄	D₂₉	1	1	yes	characteristic, complemented
19	C₂×C₄	—	29	2	no	—
20	C₂×C₄	—	29	1	no	—
21	C₂²	—	29	1	no	—
22	C₂²	C₂×D₂₉	1	2	yes	—
23	C₄	—	29	1	no	—
24	C₄	—	29	2	no	—
25	C₄	C₂×D₂₉	1	1	yes	characteristic
26	C₂	—	2	2	no	—
27	C₂	—	58	1	no	—
28	C₂	C₂²×D₂₉	1	1	yes	characteristic

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.