Subgroups — C₅×C₃₇×A₅ #26012944

Order 11100.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×A₅	C₅	1	1	yes	maximal, characteristic, direct product factor
2	C₅×A₄×C₃₇	—	5	1	no	maximal
3	C₅×D₅×C₃₇	—	6	1	no	maximal
4	C₅×D₃×C₃₇	—	10	1	no	maximal
5	C₅²×C₃₇	—	6	1	no	Hall
6	C₂²×C₅×C₃₇	—	5	1	no	—
7	C₃×C₅×C₃₇	—	10	1	no	—
8	A₄×C₃₇	—	5	1	no	Hall
9	C₂×C₅×C₃₇	—	15	1	no	—
10	D₅×C₃₇	—	6	1	no	—
11	C₅×A₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₃×C₃₇	—	10	1	no	—
13	C₅×C₃₇	—	6	1	no	—
14	C₅×C₃₇	—	12	2	no	—
15	C₅×C₃₇	A₅	1	1	yes	maximal normal, characteristic, direct product factor
16	C₂²×C₃₇	—	5	1	no	Hall
17	C₃×C₃₇	—	10	1	no	Hall
18	C₂×C₃₇	—	15	1	no	—
19	C₅×A₄	—	5	1	no	—
20	A₅	C₅×C₃₇	1	1	yes	characteristic, direct product factor
21	C₅×D₅	—	6	1	no	—
22	C₃₇	C₅×A₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₅×D₃	—	10	1	no	—
24	C₅²	—	6	1	no	Sylow
25	C₂²×C₅	—	5	1	no	—
26	C₃×C₅	—	10	1	no	—
27	A₄	—	5	1	no	Hall
28	C₂×C₅	—	15	1	no	—
29	D₅	—	6	1	no	—
30	D₃	—	10	1	no	—
31	C₅	—	6	1	no	—
32	C₅	—	12	2	no	—
33	C₅	C₃₇×A₅	1	1	yes	characteristic, direct product factor
34	C₂²	—	5	1	no	Sylow
35	C₃	—	10	1	no	Sylow
36	C₂	—	15	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.