Subgroups — C₂×(C₂₉⋊C₇)⋊D₂₉ #37555441

Order 23548.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂₉⋊C₇)⋊D₂₉	C₂	1	2	yes	maximal, direct product factor
3	C₂₉×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₉⋊D₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₂₉²	C₂×C₇	1	1	yes	characteristic, complemented
6	C₂₉⋊D₂₉	C₂×C₇	1	2	yes	complemented
7	C₂₉²	C₂²×C₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₇×D₂₉	—	29	1	no	maximal
9	C₂×D₂₉⋊C₇	—	29	1	no	maximal
10	C₂×C₇×C₂₉	—	29	1	no	—
11	C₇×D₂₉	—	29	2	no	—
12	C₂×C₂₉⋊C₇	D₂₉	1	1	yes	characteristic, complemented
13	D₂₉⋊C₇	—	29	2	no	—
14	C₇×C₂₉	—	29	1	no	—
15	C₂₉⋊C₇	C₂×D₂₉	1	1	yes	characteristic, complemented
16	C₂×D₂₉	—	29	1	no	—
17	C₂×D₂₉	—	29	1	no	—
18	C₂×D₂₉	—	203	4	no	—
19	C₂×C₂₉	—	7	4	no	—
20	C₂×C₂₉	D₂₉⋊C₇	1	1	yes	characteristic, complemented
21	C₂×C₂₉	C₇×D₂₉	1	1	yes	characteristic, complemented
22	D₂₉	—	29	2	no	—
23	D₂₉	—	29	2	no	—
24	D₂₉	—	203	8	no	—
25	C₂₉	—	7	4	no	—
26	C₂₉	C₂×D₂₉⋊C₇	1	1	yes	characteristic, complemented
27	C₂₉	C₂×C₇×D₂₉	1	1	yes	characteristic, complemented
28	C₂²×C₇	—	841	1	no	Hall
29	C₂×C₇	—	29	1	no	—
30	C₂×C₇	—	841	2	no	—
31	C₇	—	29	1	no	Sylow
32	C₂²	—	841	1	no	Sylow
33	C₂	—	841	2	no	—
34	C₂	(C₂₉⋊C₇)⋊D₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₂₉⋊C₇)⋊D₂₉
commutator, cosocle, hypocenter	C₂₉²	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₂₉²	C₂×C₇
LCS	G ▷ C₂₉²
UCS	C₁ ◁ C₂

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.