Subgroups — C₅×D₃₃₆₇ #46797604

Order 33670.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₃₆₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₄₈₁	—	7	1	no	maximal, Hall
4	C₇×C₁₃×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×D₂₅₉	—	13	1	no	maximal, Hall
6	C₅×C₁₃×C₃₇	D₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₃₇	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₄₈₁	—	7	1	no	Hall
9	C₅×D₉₁	—	37	1	no	maximal, Hall
10	D₂₅₉	—	13	1	no	Hall
11	C₁₃×C₃₇	C₅×D₇	1	1	yes	characteristic, complemented, Hall
12	C₅×C₇×C₁₃	D₃₇	1	1	yes	characteristic, complemented, Hall
13	C₅×D₃₇	—	91	1	no	Hall
14	C₇×C₃₇	C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₃₇	D₉₁	1	1	yes	characteristic, complemented, Hall
16	D₉₁	—	37	1	no	Hall
17	C₅×D₁₃	—	259	1	no	Hall
18	C₇×C₁₃	C₅×D₃₇	1	1	yes	characteristic, complemented, Hall
19	D₃₇	—	91	1	no	Hall
20	C₅×D₇	—	481	1	no	Hall
21	C₅×C₁₃	D₂₅₉	1	1	yes	characteristic, complemented, Hall
22	C₃₇	C₅×D₉₁	1	1	yes	characteristic, complemented, Sylow
23	C₅×C₇	D₄₈₁	1	1	yes	characteristic, complemented, Hall
24	D₁₃	—	259	1	no	Hall
25	D₇	—	481	1	no	Hall
26	C₁₃	C₅×D₂₅₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	3367	1	no	Hall
28	C₇	C₅×D₄₈₁	1	1	yes	characteristic, complemented, Sylow
29	C₅	D₃₃₆₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	3367	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₃₆₇
commutator, cosocle, hypocenter	C₇×C₁₃×C₃₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₃₇	C₂
LCS	G ▷ C₇×C₁₃×C₃₇
UCS	C₁ ◁ C₅

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.