Subgroups — C₂×#21439406 #29504151

Order 15276.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21439406	C₂	1	2	yes	maximal, direct product factor
2	C₂×#16838389	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#16838389	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₉×D₆₇	C₂×C₃	1	2	yes	complemented
7	C₁₉×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₆₇⋊C₃	—	19	1	no	maximal, Hall
9	C₂×C₆₇⋊C₃	—	19	1	no	—
10	D₆₇⋊C₃	—	19	2	no	—
11	C₂×D₆₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₁₉⋊C₃	—	67	1	no	maximal, Hall
13	C₆₇⋊C₃	—	19	1	no	Hall
14	C₂×C₆₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
15	D₆₇	C₂×C₁₉⋊C₃	1	2	yes	complemented
16	C₂×C₁₉⋊C₃	—	67	2	no	—
17	C₂×C₁₉⋊C₃	—	134	1	no	—
18	C₂²×C₁₉	—	67	1	no	Hall
19	C₆₇	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₁₉⋊C₃	—	134	1	no	Hall
21	C₂×C₁₉	—	67	2	no	—
22	C₂×C₁₉	D₆₇⋊C₃	1	1	yes	characteristic, complemented
23	C₁₉	C₂×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	1273	1	no	Hall
25	C₂×C₃	—	1273	2	no	—
26	C₂×C₃	—	1273	1	no	—
27	C₂²	—	67	1	no	Sylow
28	C₃	—	1273	1	no	Sylow
29	C₂	—	67	2	no	—
30	C₂	#21439406	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#21439406
commutator, cosocle, hypocenter	C₁₉×C₆₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₆₇	C₂×C₃
LCS	G ▷ C₁₉×C₆₇
UCS	C₁ ◁ C₂

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.