Subgroups — C₅×C₇⋊(C₇⋊#1181) #43249333

Order 28420.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊(C₇⋊#1181)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇⋊#1181	—	7	8	no	maximal
5	C₇²×D₂₉	C₂×C₅	1	1	yes	characteristic
6	C₅×C₇×D₂₉	D₇	1	8	yes	—
7	C₇²×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₂₉	Dic₇	1	8	yes	complemented
9	C₅×C₇⋊Dic₇	—	29	1	no	maximal, Hall
10	C₇⋊#1181	—	7	8	no	—
11	C₅×#1181	—	49	1	no	Hall
12	C₂×C₅×C₇²	—	29	1	no	—
13	C₇×D₂₉	C₅×D₇	1	8	yes	—
14	C₅×D₂₉	C₇⋊D₇	1	1	yes	characteristic
15	C₅×C₇²	#1181	1	1	yes	characteristic, complemented, Hall
16	C₇×C₂₉	C₅×Dic₇	1	8	yes	complemented
17	C₇⋊Dic₇	—	29	1	no	Hall
18	C₅×C₂₉	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
19	C₅×Dic₇	—	203	8	no	—
20	#1181	—	49	1	no	Hall
21	C₂×C₇²	—	29	1	no	—
22	C₂×C₅×C₇	—	29	8	no	—
23	D₂₉	C₅×C₇⋊D₇	1	1	yes	characteristic
24	C₇²	C₅×#1181	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₇	C₇⋊#1181	1	8	yes	complemented
26	C₂₉	C₅×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
27	Dic₇	—	203	8	no	—
28	C₄×C₅	—	1421	1	no	Hall
29	C₂×C₇	—	29	8	no	—
30	C₂×C₅	—	29	1	no	—
31	C₇	C₅×C₇⋊#1181	1	8	yes	complemented
32	C₅	C₇⋊(C₇⋊#1181)	1	1	yes	characteristic, direct product factor, Sylow
33	C₄	—	1421	1	no	Sylow
34	C₂	—	29	1	no	—

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.