Subgroups — C₄₉⋊#10596817 #43249263

Order 28420.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₉×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₉×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₉⋊#1181	—	5	1	no	maximal, Hall
4	C₇⋊#10596817	—	7	1	no	maximal
5	C₄₉×D₂₉	D₅	1	1	yes	characteristic
6	C₅×C₇×D₂₉	D₇	1	1	yes	characteristic
7	C₂₉×C₄₉	Dic₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₂₉	Dic₇	1	1	yes	characteristic
9	Dic₂₄₅	—	29	1	no	maximal, Hall
10	C₇⋊#1181	—	35	1	no	—
11	#10596817	—	49	1	no	Hall
12	C₂×C₅×C₄₉	—	29	1	no	—
13	C₇×D₂₉	D₃₅	1	1	yes	characteristic
14	C₅×D₂₉	D₄₉	1	1	yes	characteristic
15	C₅×C₄₉	#1181	1	1	yes	characteristic, complemented, Hall
16	C₇×C₂₉	Dic₃₅	1	1	yes	characteristic
17	Dic₄₉	—	145	1	no	Hall
18	C₅×C₂₉	Dic₄₉	1	1	yes	characteristic, complemented, Hall
19	Dic₃₅	—	203	1	no	—
20	#1181	—	245	1	no	Hall
21	C₂×C₄₉	—	29	1	no	—
22	C₂×C₅×C₇	—	29	1	no	—
23	D₂₉	D₂₄₅	1	1	yes	characteristic
24	C₄₉	#10596817	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₇	C₇⋊#1181	1	1	yes	characteristic
26	C₂₉	Dic₂₄₅	1	1	yes	characteristic, complemented, Sylow
27	Dic₇	—	1015	1	no	—
28	Dic₅	—	1421	1	no	Hall
29	C₂×C₇	—	29	1	no	—
30	C₂×C₅	—	29	1	no	—
31	C₇	C₇⋊#10596817	1	1	yes	characteristic
32	C₅	C₄₉⋊#1181	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	7105	1	no	Sylow
34	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₂₉×C₄₉	C₄
Frattini	C₇	C₇⋊#10596817
socle	C₅×C₇×C₂₉	Dic₇
prime radical	C₅×C₇×D₂₉	D₇
cosocle	C₅×C₄₉×D₂₉	C₂
LCS	G ▷ C₅×C₂₉×C₄₉
UCS	C₁

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.