Subgroups — C₅×A₅×C₁₀₇ #44545717

Order 32100.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₅×C₁₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor
2	C₅×A₄×C₁₀₇	—	5	1	no	maximal
3	C₅×D₅×C₁₀₇	—	6	1	no	maximal
4	C₅×D₃×C₁₀₇	—	10	1	no	maximal
5	C₅²×C₁₀₇	—	6	1	no	Hall
6	C₂²×C₅×C₁₀₇	—	5	1	no	—
7	C₃×C₅×C₁₀₇	—	10	1	no	—
8	A₄×C₁₀₇	—	5	1	no	Hall
9	C₂×C₅×C₁₀₇	—	15	1	no	—
10	D₅×C₁₀₇	—	6	1	no	—
11	D₃×C₁₀₇	—	10	1	no	—
12	C₅×C₁₀₇	—	6	1	no	—
13	C₅×C₁₀₇	—	12	2	no	—
14	C₅×C₁₀₇	A₅	1	1	yes	maximal normal, characteristic, direct product factor
15	C₂²×C₁₀₇	—	5	1	no	Hall
16	C₃×C₁₀₇	—	10	1	no	Hall
17	C₅×A₅	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₁₀₇	—	15	1	no	—
19	C₁₀₇	C₅×A₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₅×A₄	—	5	1	no	—
21	A₅	C₅×C₁₀₇	1	1	yes	characteristic, direct product factor
22	C₅×D₅	—	6	1	no	—
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	A₅×C₁₀₇	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.