Subgroups — C₅×#20299800 #49136405

Order 36260.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#20299800	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃₇×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic
5	C₅×D₇×C₃₇	—	14	4	no	—
6	C₇²×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₃₇	—	2	4	no	—
8	C₅×#5997	—	37	1	no	maximal, Hall
9	C₅×Dic₃₇	—	49	1	no	maximal, Hall
10	D₇×C₃₇	—	14	4	no	—
11	C₅×C₇⋊D₇	D₃₇	1	1	yes	characteristic
12	C₂×C₅×C₃₇	—	49	1	no	—
13	C₇×C₃₇	—	2	4	no	—
14	C₅×C₇²	Dic₃₇	1	1	yes	characteristic, complemented, Hall
15	#5997	—	37	1	no	Hall
16	C₅×C₃₇	#5997	1	1	yes	characteristic, complemented, Hall
17	Dic₃₇	—	49	1	no	Hall
18	C₇⋊D₇	C₅×D₃₇	1	1	yes	characteristic
19	C₂×C₃₇	—	49	1	no	—
20	C₅×D₇	—	14	4	no	—
21	C₇²	C₅×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
22	C₃₇	C₅×#5997	1	1	yes	characteristic, complemented, Sylow
23	C₅×C₇	—	2	4	no	—
24	C₄×C₅	—	1813	1	no	Hall
25	D₇	—	14	4	no	—
26	C₂×C₅	—	49	1	no	—
27	C₇	—	2	4	no	—
28	C₅	#20299800	1	1	yes	characteristic, direct product factor, Sylow
29	C₄	—	1813	1	no	Sylow
30	C₂	—	49	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.